Title: Approximate identities and stability of discrete convolution operators with flip
Abstract: A sequence {A λ}λ∈Λ of linear bounded operators is called stable if for all sufficiently large λ the inverses of Aλ exist and their norms are uniformly bounded. We consider the stability problem for sequences {A λ{λ∈Λ arising from discrete convolution operators with flip and generating functions k λ a where a is a piecewise continuous function on the unit circle and k λ is an approximate identity. The main result is that a sequence of operators belonging to a certain C*-algebra is stable if and only if a certain collection of operators is invertible. As an application we discuss several concrete examples, for instance, Toeplitz + Hankel operators and singular integral operators with flip.
Publication Year: 1999
Publication Date: 1999-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 11
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