Alain Guichardet, mathematician

Guichardet is a prolific writer and researcher with a modern view of mathematics. He suggested in 1967 a possible definition of continuous tensor product, which posed the question, when does the continuous tensor product of Hilbert spaces exist? The answer to this, in the context of representation theory of groups, Lie algebras and Hopf algebras, has led to a large amount of insight into quantum field theory and classical and quantum stochastic processes. In this paper Dan Dubin and I show that continuous tensor products of representations of Lie algebras do not always exist. The same result is more carefully described in "Sur les produits tensoriels continus des espaces hilbertiens", by A. Guichardet and A. Wulfsohn, Jour. Funct. Anal. , 2, 371-377, 1968.

A very clear and detailed account of Guichardet's approach can be found in his book, "Symmetric Hilbert Spaces and Related Topics", Springer Lecture Notes in Maths., 261, 1972.