Lionel Cooper (mathematician)

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Lionel Cooper

Jacob Lionel Bakst Cooper.jpg

JLB Cooper, c.1960
Born(1915-12-27)27 December 1915
Beaufort West, Western Cape, South Africa
Died 8 August 1979(1979-08-08) (aged 63)
London, England
Nationality South African
Alma mater University of Cape Town
Queen's College, Oxford
Awards Berwick Prize (1949)
Scientific career
Fields operator theory, transform theory, thermodynamics, functional analysis and differential equations
Institutions Birkbeck College
Imperial College
Cardiff University
University of Witwatersrand
University of Toronto.
Chelsea College, University of London
Doctoral advisor Edward Titchmarsh
Doctoral students James Stewart

Jacob Lionel Bakst Cooper (27 December 1915 – 8 August 1979) was a South African mathematician who worked in operator theory, transform theory, thermodynamics, functional analysis and differential equations.

South Africa Republic in the southernmost part of Africa

South Africa, officially the Republic of South Africa (RSA), is the southernmost country in Africa. It is bounded to the south by 2,798 kilometres (1,739 mi) of coastline of Southern Africa stretching along the South Atlantic and Indian Oceans; to the north by the neighbouring countries of Namibia, Botswana, and Zimbabwe; and to the east and northeast by Mozambique and Eswatini (Swaziland); and it surrounds the enclaved country of Lesotho. South Africa is the largest country in Southern Africa and the 25th-largest country in the world by land area and, with over 57 million people, is the world's 24th-most populous nation. It is the southernmost country on the mainland of the Old World or the Eastern Hemisphere. About 80 percent of South Africans are of Sub-Saharan African ancestry, divided among a variety of ethnic groups speaking different African languages, nine of which have official status. The remaining population consists of Africa's largest communities of European (White), Asian (Indian), and multiracial (Coloured) ancestry.

In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis.

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.



Cooper was born in Beaufort West, Western Cape, South Africa. Following the death of his father in 1919, the family moved to Cape Town 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. [1]

Cape Town Capital city of the Western Cape province and legislative capital of South Africa

Cape Town is the oldest city in South Africa, colloquially named the Mother City. It is the legislative capital of South Africa and primate city of the Western Cape province. It forms part of the City of Cape Town metropolitan municipality.

South African College Schools primary and secondary education institution in Newlands, Cape Town, South Africa

The South African College Schools is a primary and secondary education institution in Newlands, Cape Town, South Africa. Founded in 1829, it is the oldest school in South Africa. SACS is one of four schools expressly named by Cecil John Rhodes to offer an annual Rhodes Scholarship to one of its graduating students. The schools are a combination of the South African College Junior School and the South African College High School.

In Judaism, a rabbi is a teacher of Torah. The basic form of the rabbi developed in the Pharisaic and Talmudic era, when learned teachers assembled to codify Judaism's written and oral laws. The first sage for whom the Mishnah uses the title of rabbi was Yohanan ben Zakkai, active in the early-to-mid first century CE. In more recent centuries, the duties of a rabbi became increasingly influenced by the duties of the Protestant Christian minister, hence the title "pulpit rabbis", and in 19th-century Germany and the United States rabbinic activities including sermons, pastoral counseling, and representing the community to the outside, all increased in importance.

He won a Rhodes Scholarship to Oxford and started to study at Queen's College in 1935, [2] obtaining his D.Phil. in 1940 under the supervision of Edward Charles Titchmarsh. [3] 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.

Rhodes Scholarship an international postgraduate award for students to study at the University of Oxford

The Rhodes Scholarship is an international postgraduate award for students to study at the University of Oxford. It was established in 1902, making it the first large-scale programme of international scholarship. The Rhodes Scholarship was founded by English businessman and politician Cecil John Rhodes, to promote unity between English speaking nations and instill a sense of civic-minded leadership and moral fortitude in future leaders irrespective of their chosen career paths. Although initially restricted to male applicants from countries which are today within the Commonwealth, as well as Germany and the United States, today the Scholarship is open to applicants from all backgrounds and from across the globe. Since its creation, controversy has surrounded both its former exclusion of women, and Rhodes' Anglo-supremacist beliefs and legacy of colonialism.

Doctor of Philosophy Postgraduate academic degree awarded by universities in many countries

A Doctor of Philosophy is the highest university degree that is conferred after a course of study by universities in most English-speaking countries. PhDs are awarded for programs across the whole breadth of academic fields. As an earned research degree, those studying for a PhD are usually required to produce original research that expands the boundaries of knowledge, normally in the form of a thesis or dissertation, and defend their work against experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title Doctor or, in non-English-speaking countries, variants such as "Dr. phil." with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at universities or work in academic, educational, or research fields are usually addressed by this title "professionally and socially in a salutation or conversation." Alternatively, holders may use post-nominal letters such as "Ph.D.", "PhD", or "DPhil". It is, however, considered incorrect to use both the title and post-nominals at the same time.

Edward Charles "Ted" Titchmarsh was a leading English mathematician.

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.

Bristol Aeroplane Company 1910-1959 aerospace manufacturer in the United Kingdom

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 aircraft produced by the company include the 'Boxkite', the Bristol Fighter, the Bulldog, the Blenheim, the Beaufighter, and the Britannia, and much of the preliminary work which led to the Concorde was carried out by the company. In 1956 its major operations were split into Bristol Aircraft and Bristol Aero Engines. In 1959, Bristol Aircraft merged with several major British aircraft companies to form the British Aircraft Corporation (BAC) and Bristol Aero Engines merged with Armstrong Siddeley to form Bristol Siddeley.

Russia transcontinental country in Eastern Europe and Northern Asia

Russia, officially the Russian Federation, is a transcontinental country in Eastern Europe and North Asia. At 17,125,200 square kilometres (6,612,100 sq mi), Russia is by a considerable margin the largest country in the world by area, covering more than one-eighth of the Earth's inhabited land area, and the ninth most populous, with about 146.77 million people as of 2019, including Crimea. About 77% of the population live in the western, European part of the country. Russia's capital, Moscow, is one of the largest cities in the world and the second largest city in Europe; other major cities include Saint Petersburg, Novosibirsk, Yekaterinburg and Nizhny Novgorod. Extending across the entirety of Northern Asia and much of Eastern Europe, Russia spans eleven time zones and incorporates a wide range of environments and landforms. From northwest to southeast, Russia shares land borders with Norway, Finland, Estonia, Latvia, Lithuania and Poland, Belarus, Ukraine, Georgia, Azerbaijan, Kazakhstan, China, Mongolia and North Korea. It shares maritime borders with Japan by the Sea of Okhotsk and the U.S. state of Alaska across the Bering Strait. However, Russia recognises two more countries that border it, Abkhazia and South Ossetia, both of which are internationally recognized as parts of Georgia.

Academic career

From 1944 he lectured at Birkbeck College 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.

Birkbeck, University of London public research university located in Bloomsbury, London, England

Birkbeck, University of London, is a public research university located in Bloomsbury London, England, and a constituent college of the federal University of London. Established in 1823 as the London Mechanics' Institute by its founder, Sir George Birkbeck, and its supporters, Jeremy Bentham, J. C. Hobhouse and Henry Brougham, Birkbeck has been one of the few institutions to specialise in evening higher education.

Albert Einstein German-born physicist and developer of the theory of relativity

Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics. His work is also known for its influence on the philosophy of science. He is best known to the general public for his mass–energy equivalence formula E = mc2, which has been dubbed "the world's most famous equation". He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory.

Quantum mechanics branch of physics dealing with phenomena at scales of the order of the Planck constant

Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

In 1951 he was appointed professor at the Cardiff University [2] 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.

Cardiff University public research university in Cardiff, Wales, United Kingdom

Cardiff University is a public research university in Cardiff, Wales. Founded in 1883 as the University College of South Wales and Monmouthshire, it became one of the founding colleges of the University of Wales in 1893, and in 1997 received its own degree-awarding powers. It merged with the University of Wales Institute of Science and Technology (UWIST) in 1988. The college adopted the public name of Cardiff University in 1999, and in 2005 this became its legal name, when it became an independent university awarding its own degrees. The third oldest university institution in Wales, it is composed of three colleges: Arts, Humanities and Social Sciences; Biomedical and Life Sciences; and Physical Sciences and Engineering.

London Mathematical Society

The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics.

California Institute of Technology private research university located in Pasadena, California

The California Institute of Technology (Caltech) is a private doctorate-granting research university in Pasadena, California. Known for its strength in natural science and engineering, Caltech is often ranked as one of the world's top-ten universities.

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.


Within operator theory, Cooper worked in the area of linear operators on real or complex Hilbert spaces. He studied the unbounded operators that arose from quantum theory, [2] 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 transformations that satisfy functional relations arising from representations of linear groups. [2] In this he collaborated closely with P.L. Butzer of RWTH Aachen.

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  1. Edmunds D.E: Jacob Lionel Bakst Cooper, Bull London Math. Soc., 13 1981 pp 429-450
  2. 1 2 3 4 O'Connor, J. J.; Robertson, E. F. (December 1996). "Jacob Lionel Bakst Cooper". MacTutor. Retrieved 2008-10-15.
  3. "Jacob Lionel Bakst Cooper". Mathematics Genealogy Project. Retrieved 2008-10-15.