After school in Cape Town, South Africa, Lionel Cooper went to the University of Cape Town in 1932. He graduated with a degree in mathematics and physics having won numerous prizes in pure mathematics, applied mathematics and history. He then won a scholarship to study at Queen's College, Oxford and he began his studies there in 1935. Again he won prizes and a distinction in the theory of functions.
A research scholarship enabled him to work for a D.Phil. under Titchmarsh's supervision. The degree was awarded in 1940 for the thesis Theory and applications of Fourier integrals. From 1940 to 1944 he worked with the Bristol Aeroplane Company having failed the medical to serve in the armed forces. After lecturing in London (both at Birkbeck College and Imperial College) he was appointed professor of mathematics in Cardiff in 1951. After moving to Toronto in 1965 he returned to England two years later.
His research is on a wide range of different but related topics: operator theory, transform theory, thermodynamics, functional analysis and differential equations.
Cooper's work in operator theory was in the area of linear operators on real or complex Hilbert spaces. He studied the unbounded operators which arose from quantum theory. He corresponded with Einstein on logical inconsistency in quantum theory in 1949.
In the area of transform theory he worked on the representation and uniqueness of integral transforms, on approximation, and on linear transformations which satisfy functional relations arising from representations of transformation groups.
His lecturing is described in  as follows:-
As a lecturer he could be hard to follow: sometimes the sequence of ideas came too quickly for the comfort of those in the audience with less agile minds: sometimes he overestimated the background knowledge of his audience. However, many of his lectures were enormously stimulating and were full of unexpected insights into the topics being studied.References (2 books/articles)
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