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The Fourier binest algebra.

Research output: Contribution to journalJournal article

Published

Journal publication date11/1997
JournalMathematical Proceedings of the Cambridge Philosophical Society
Journal number3
Volume122
Number of pages15
Pages525-539
Original languageEnglish

Abstract

The Fourier binest algebra is defined as the intersection of the Volterra nest algebra on L2([open face R]) with its conjugate by the Fourier transform. Despite the absence of nonzero finite rank operators this algebra is equal to the closure in the weak operator topology of the Hilbert–Schmidt bianalytic pseudo-differential operators. The (non-distributive) invariant subspace lattice is determined as an augmentation of the Volterra and analytic nests (the Fourier binest) by a continuum of nests associated with the unimodular functions exp([minus sign]isx2/2) for s>0. This multinest is the reflexive closure of the Fourier binest and, as a topological space with the weak operator topology, it is shown to be homeomorphic to the unit disc. Using this identification the unitary automorphism group of the algebra is determined as the semi-direct product [open face R]2×[kappa][open face R] for the action [kappa]t([lambda], [mu]) =(et[lambda], e[minus sign]t [mu]).

Bibliographic note

http://journals.cambridge.org/action/displayJournal?jid=PSP The final, definitive version of this article has been published in the Journal, Mathematical Proceedings of the Cambridge Philosophical Society, 122 (3), pp 525-539 1997, © 1997 Cambridge University Press.