Constructive Thoughts on Operator Algebras

25 mins 1 sec, 346.76 MB, MPEG-4 Video 640x360, 29.97 fps, 44100 Hz, 1.84 Mbits/sec

About this item

Description:	Bridges, D (University of Canterbury) Tuesday 24 January 2012, 16:30-17:00


Created:	2012-01-27 09:58
Collection:	Semantics and Syntax: A Legacy of Alan Turing
Publisher:	Isaac Newton Institute
Copyright:	Bridges, D
Language:	eng (English)


Abstract:	Operator algebra theory, in its classical form, is developed in about as nonconstructive a manner as one could imagine: typical existence proofs use contradiction arguments and applications of Zorn's lemma. Finding a viable constructive development of, or perhaps alternative to, operator algebra theory would seem to be a major test of Bishop-style constructive mathematics (or, indeed, of any other approach to extracting the computational content of a classical theory). In my talk I shall present some of the background, some recent progress, and some of the major problems that lie at the very start of such a development.

Abstract:

Operator algebra theory, in its classical form, is developed in about as nonconstructive a manner as one could imagine: typical existence proofs use contradiction arguments and applications of Zorn's lemma. Finding a viable constructive development of, or perhaps alternative to, operator algebra theory would seem to be a major test of Bishop-style constructive mathematics (or, indeed, of any other approach to extracting the computational content of a classical theory). In my talk I shall present some of the background, some recent progress, and some of the major problems that lie at the very start of such a development.

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