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Lionel Cooper (mathematician)
Encyclopedia
Jacob Lionel Bakst Cooper (born 27 December 1915, Beaufort West
, Cape Province
, South Africa
, died 8 August 1979, London
, England
) was a South Africa
n mathematician who worked in operator theory
, transform theory
, thermodynamics
, functional analysis
and differential equations.
where he attended the South African College School
. His ability was soon recognized and he was encouraged to become a rabbi
. However he rejected the Jewish faith and instead studied mathematics
and physics
at the University of Cape Town
, where he won the Governor General’s prize for pure mathematics. He took an active part in student politics becoming a socialist member of the Student’s Parliament, with strong views against racism
and Nazism
.
He won a Rhodes Scholarship
to Oxford and started to study at Queen's College in 1935, obtaining his D.Phil.
in 1940 under the supervision of Edward Charles Titchmarsh
. His work made an immediate impact and as early as January 1939 he was invited to speak at Hadamard’s seminar in the Collège de France
.
While in Oxford he joined the Communist party, where he met his future wife Kathleen Dixon. Turned down for active service due to his poor eyesight, he worked for the Bristol Aeroplane Company
from 1940 to 1944. During this time he became disenchanted with Russia
’s non-aggression pact
with the Nazis and left the Communist party.
and for a short time Imperial College, and was awarded the Berwick Prize
in 1949. His correspondence of that year included two letters from Albert Einstein
concerning possible logical inconsistencies in quantum mechanics
.
In 1951 he was appointed professor at the Cardiff University
where he stayed until 1963 apart from a break in 1954 when he spent some time in the University of Witwatersrand. From 1952 to 1959 he edited the proceedings of the London Mathematical Society
. After leaving Cardiff he spent three years in North America, as visiting professor at Caltech
during 1964, followed by a two year stay at the University of Toronto
. While in Toronto he edited the Canadian Journal of Mathematics
.
In 1967 he returned to the UK to serve as head of the mathematics department at the newly constituted Chelsea College, University of London, where he remained until his death.
s. He studied the unbounded operator
s that arose from quantum theory
, extending basic work of Frigyes Riesz
and John von Neumann
.
Within transform theory, he worked on the representation and uniqueness of integral transforms, on approximation, and on linear transformation
s that satisfy functional relations arising from representations
of linear groups. In this he collaborated closely with P.L. Butzer of RWTH Aachen
.
Beaufort West
Beaufort West is a town in the Western Cape province in South Africa. It is the largest town in the arid Great Karoo region, and forms part of the Beaufort West Local Municipality, with 37 000 inhabitants in 2001....
, Cape Province
Cape Province
The Province of the Cape of Good Hope was a province in the Union of South Africa and subsequently the Republic of South Africa...
, South Africa
South Africa
The Republic of South Africa is a country in southern Africa. Located at the southern tip of Africa, it is divided into nine provinces, with of coastline on the Atlantic and Indian oceans...
, died 8 August 1979, London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
) was a South Africa
South Africa
The Republic of South Africa is a country in southern Africa. Located at the southern tip of Africa, it is divided into nine provinces, with of coastline on the Atlantic and Indian oceans...
n mathematician who worked in operator theory
Operator theory
In mathematics, operator theory is the branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators.Operator theory also includes the study of algebras of operators....
, transform theory
Transform theory
In mathematics, transform theory is the study of transforms. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or diagonalized as in spectral theory.-Spectral theory:...
, thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
and differential equations.
Development
Cooper was born in Beaufort West, Cape Province, South Africa. Following the death of his father in 1919, the family moved to Cape TownCape Town
Cape Town is the second-most populous city in South Africa, and the provincial capital and primate city of the Western Cape. As the seat of the National Parliament, it is also the legislative capital of the country. It forms part of the City of Cape Town metropolitan municipality...
where he attended the South African College School
South African College Schools
The South African College Schools, commonly referred to as SACS, is a primary and secondary education institution located in Newlands, Cape Town, South Africa. Founded in 1829, it is the oldest school in South Africa and one of four schools expressly named by Cecil John Rhodes to offer an annual...
. His ability was soon recognized and he was encouraged to become a rabbi
Rabbi
In Judaism, a rabbi is a teacher of Torah. This title derives from the Hebrew word רבי , meaning "My Master" , which is the way a student would address a master of Torah...
. However he rejected the Jewish faith and instead studied mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
at the University of Cape Town
University of Cape Town
The University of Cape Town is a public research university located in Cape Town in the Western Cape province of South Africa. UCT was founded in 1829 as the South African College, and is the oldest university in South Africa and the second oldest extant university in Africa.-History:The roots of...
, where he won the Governor General’s prize for pure mathematics. He took an active part in student politics becoming a socialist member of the Student’s Parliament, with strong views against racism
Racism
Racism is the belief that inherent different traits in human racial groups justify discrimination. In the modern English language, the term "racism" is used predominantly as a pejorative epithet. It is applied especially to the practice or advocacy of racial discrimination of a pernicious nature...
and Nazism
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
.
He won a Rhodes Scholarship
Rhodes Scholarship
The Rhodes Scholarship, named after Cecil Rhodes, is an international postgraduate award for study at the University of Oxford. It was the first large-scale programme of international scholarships, and is widely considered the "world's most prestigious scholarship" by many public sources such as...
to Oxford and started to study at Queen's College in 1935, obtaining his D.Phil.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1940 under the supervision of Edward Charles Titchmarsh
Edward Charles Titchmarsh
Edward Charles "Ted" Titchmarsh was a leading British mathematician.He was educated at King Edward VII School and Balliol College, Oxford, where he began his studies in October 1917....
. His work made an immediate impact and as early as January 1939 he was invited to speak at Hadamard’s seminar in the Collège de France
Collège de France
The Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles...
.
While in Oxford he joined the Communist party, where he met his future wife Kathleen Dixon. Turned down for active service due to his poor eyesight, he worked for the Bristol Aeroplane Company
Bristol Aeroplane Company
The Bristol Aeroplane Company, originally the British and Colonial Aeroplane Company, was both one of the first and one of the most important British aviation companies, designing and manufacturing both airframes and aero engines...
from 1940 to 1944. During this time he became disenchanted with Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
’s non-aggression pact
Molotov-Ribbentrop Pact
The Molotov–Ribbentrop Pact, named after the Soviet foreign minister Vyacheslav Molotov and the German foreign minister Joachim von Ribbentrop, was an agreement officially titled the Treaty of Non-Aggression between Germany and the Soviet Union and signed in Moscow in the late hours of 23 August 1939...
with the Nazis and left the Communist party.
Academic career
From 1944 he lectured at Birkbeck CollegeBirkbeck, University of London
Birkbeck, University of London is a public research university located in London, United Kingdom and a constituent college of the federal University of London. It offers many Master's and Bachelor's degree programmes that can be studied either part-time or full-time, though nearly all teaching is...
and for a short time Imperial College, and was awarded the Berwick Prize
Berwick Prizes
The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the society to establish two prizes...
in 1949. His correspondence of that year included two letters from Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
concerning possible logical inconsistencies in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.
In 1951 he was appointed professor at the Cardiff University
Cardiff University
Cardiff University is a leading research university located in the Cathays Park area of Cardiff, Wales, United Kingdom. It received its Royal charter in 1883 and is a member of the Russell Group of Universities. The university is consistently recognised as providing high quality research-based...
where he stayed until 1963 apart from a break in 1954 when he spent some time in the University of Witwatersrand. From 1952 to 1959 he edited the proceedings of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
. After leaving Cardiff he spent three years in North America, as visiting professor at Caltech
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
during 1964, followed by a two year stay at the University of Toronto
University of Toronto
The University of Toronto is a public research university in Toronto, Ontario, Canada, situated on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution of higher learning in Upper Canada...
. While in Toronto he edited the Canadian Journal of Mathematics
Canadian Journal of Mathematics
The Canadian Journal of Mathematics is a bimonthly mathematics journal published by the Canadian Mathematical Society. It was established in 1949 by H.S.M. Coxeter and G. de B. Robinson. The current editors of the journal are Henry Kim and Robert McCann. The journal publishes articles in all...
.
In 1967 he returned to the UK to serve as head of the mathematics department at the newly constituted Chelsea College, University of London, where he remained until his death.
Mathematics
Within operator theory, Cooper worked in the area of linear operators on real or complex Hilbert spaceHilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
s. He studied the unbounded operator
Unbounded operator
In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases....
s that arose from quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, extending basic work of Frigyes Riesz
Frigyes Riesz
Frigyes Riesz was a mathematician who was born in Győr, Hungary and died in Budapest, Hungary. He was rector and professor at University of Szeged...
and John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
.
Within transform theory, he worked on the representation and uniqueness of integral transforms, on approximation, and on linear transformation
Linear transformation
In mathematics, a linear map, linear mapping, linear transformation, or linear operator is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. As a result, it always maps straight lines to straight lines or 0...
s that satisfy functional relations arising from representations
Group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication...
of linear groups. In this he collaborated closely with P.L. Butzer of RWTH Aachen
RWTH Aachen
RWTH Aachen University is a research university located in Aachen, North Rhine-Westphalia, Germany with roughly 33,000 students enrolled in 101 study programs....
.