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Approximate Identities, Almost-Periodic Functions and Toeplitz Operators

Approximate Identities, Almost-Periodic Functions and Toeplitz Operators A sequence {A λ}λ∈Λ of linear bounded operators is called stable if, for all sufficiently large λ, the inverses of A λ exist and their norms are uniformly bounded. We consider the stability problem for sequences of Toeplitz operators {T(k λ a)}λ∈Λ, where a(t) is an almost-periodic function on unit circle and k λ a is an approximate identity. A stability criterion is established in terms of the invertibility of a family of almost-periodic functions. This family of functions depends on the approximate identity used in a very subtle way, and the stability condition is, in general, stronger than the invertibility condition of the Toeplitz operator T(a). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Approximate Identities, Almost-Periodic Functions and Toeplitz Operators

Acta Applicandae Mathematicae , Volume 65 (3) – Oct 19, 2004

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1010609706382
Publisher site
See Article on Publisher Site

Abstract

A sequence {A λ}λ∈Λ of linear bounded operators is called stable if, for all sufficiently large λ, the inverses of A λ exist and their norms are uniformly bounded. We consider the stability problem for sequences of Toeplitz operators {T(k λ a)}λ∈Λ, where a(t) is an almost-periodic function on unit circle and k λ a is an approximate identity. A stability criterion is established in terms of the invertibility of a family of almost-periodic functions. This family of functions depends on the approximate identity used in a very subtle way, and the stability condition is, in general, stronger than the invertibility condition of the Toeplitz operator T(a).

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 19, 2004

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