Jacob Lionel Bakst Cooper (27 December 1915 – 8 August 1979) was a South African mathematician who worked in operator theory,

transform theory In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be sim ...

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

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 (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

and

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

Development

Cooper was born in Beaufort West, Western Cape, South Africa. Following the death of his father in 1919, the family moved to

Cape Town Cape Town ( af, Kaapstad; , xh, iKapa) is one of South Africa's three capital cities, serving as the seat of the Parliament of South Africa. It is the legislative capital of the country, the oldest city in the country, and the second largest ...

where he attended the

South African College School The South African College Schools (colloquially often known as “SACS”) is a public English medium primary and high education institution situated in Newlands - part of the Southern Suburbs region of Cape Town in the Western Cape province of ...

. His ability was soon recognized and he was encouraged to become a

rabbi A rabbi () is a spiritual leader or religious teacher in Judaism. One becomes a rabbi by being ordained by another rabbi – known as ''semikha'' – following a course of study of Jewish history and texts such as the Talmud. The basic form of ...

. However he rejected the Jewish faith and instead studied

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

at the

University of Cape Town The University of Cape Town (UCT) ( af, Universiteit van Kaapstad, xh, Yunibesithi ya yaseKapa) is a public research university in Cape Town, South Africa. Established in 1829 as the South African College, it was granted full university statu ...

, 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 is the belief that groups of humans possess different behavioral traits corresponding to inherited attributes and can be divided based on the superiority of one race over another. It may also mean prejudice, discrimination, or antagonism ...

and

Nazism Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Na ...

. He won a

Rhodes Scholarship The Rhodes Scholarship is an international postgraduate award for students to study at the University of Oxford, in the United Kingdom. Established in 1902, it is the oldest graduate scholarship in the world. It is considered among the world' ...

Oxford Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

and started to study at Queen's College in 1935, obtaining his

D.Phil. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1940 under the supervision of

Edward Charles Titchmarsh Edward Charles "Ted" Titchmarsh (June 1, 1899 – January 18, 1963) was a leading British mathematician. Education Titchmarsh was educated at King Edward VII School (Sheffield) and Balliol College, Oxford, where he began his studies in October ...

. 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 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 aircraft engines. Notable a ...

from 1940 to 1944. During this time he became disenchanted with

Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...

's non-aggression pact with the Nazis and left the Communist party.

Academic career

From 1944 he lectured at

Birkbeck College Birkbeck, University of London (formally Birkbeck College, University of London), is a public university, public research university, located in Bloomsbury, London, England, and a constituent college, member institution of the federal Universit ...

and for a short time

Imperial College Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...

, and was awarded the

Berwick Prize 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 ...

in 1949. His correspondence of that year included two letters from

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...

concerning possible logical inconsistencies in

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

. In 1951 he was appointed professor at the

Cardiff University , latin_name = , image_name = Shield of the University of Cardiff.svg , image_size = 150px , caption = Coat of arms of Cardiff University , motto = cy, Gwirionedd, Undod a Chytgord , mottoeng = Truth, Unity and Concord , established = 1 ...

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 The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

. After leaving Cardiff he spent three years in North America, as visiting professor at

Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

during 1964, followed by a two-year stay at the

University of Toronto The University of Toronto (UToronto or U of T) is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution ...

. While in Toronto he edited the

Canadian Journal of Mathematics The ''Canadian Journal of Mathematics'' (french: Journal canadien de mathématiques) 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 cur ...

. 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 operator In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pre ...

s on real or complex

Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...

s. He studied the unbounded operators that arose from

quantum theory Quantum theory may refer to: Science *Quantum mechanics, a major field of physics *Old quantum theory, predating modern quantum mechanics * Quantum field theory, an area of quantum mechanics that includes: ** Quantum electrodynamics ** Quantum ch ...

, extending basic work of

Frigyes Riesz Frigyes Riesz ( hu, Riesz Frigyes, , sometimes spelled as Frederic; 22 January 1880 – 28 February 1956) was a HungarianEberhard Zeidler: Nonlinear Functional Analysis and Its Applications: Linear monotone operators. Springer, 199/ref> mathema ...

and

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

. Within transform theory, he worked on the representation and uniqueness of integral transforms, on approximation, and on linear transformations that satisfy functional relations arising from representations of linear groups. In this he collaborated closely with P.L. Butzer of RWTH Aachen.

References

{{DEFAULTSORT:Cooper, Lionel 1915 births 1979 deaths People from Beaufort West 20th-century South African mathematicians South African mathematicians University of Cape Town alumni Alumni of The Queen's College, Oxford Academics of Birkbeck, University of London Academics of Imperial College London Academics of Cardiff University Academic staff of the University of Toronto South African Rhodes Scholars