TY - JOUR

T1 - The Fourier binest algebra.

AU - Power, Stephen C.

AU - Katavolos, A.

N1 - 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.

PY - 1997/11

Y1 - 1997/11

N2 - 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]).

AB - 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]).

U2 - 10.1017/S0305004197001965

DO - 10.1017/S0305004197001965

M3 - Journal article

VL - 122

SP - 525

EP - 539

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -