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The Fourier binest algebra.

Power, Stephen C. and Katavolos, A. (1997) The Fourier binest algebra. Mathematical Proceedings of the Cambridge Philosophical Society, 122 (3). pp. 525-539. ISSN 0305-0041

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    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]).

    Item Type: Article
    Journal or Publication Title: Mathematical Proceedings of the Cambridge Philosophical Society
    Additional Information: 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.
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 19509
    Deposited By: ep_ss_importer
    Deposited On: 14 Nov 2008 12:15
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 13:12
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/19509

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