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Algebras of approximation sequences: Fredholm theory in fractal algebras

100%
Roch S.
Studia Mathematica
|
2002
|
tom 150
|
nr 1
53-77
EN
The present paper is a continuation of [5, 7] where a Fredholm theory for approximation sequences is proposed and some of its properties and consequences are studied. Here this theory is specified to the class of fractal approximation methods. The main result is a formula for the so-called α-number of an approximation sequence (Aₙ) which is the analogue of the kernel dimension of a Fredholm operator.
2
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Finite sections of truncated Toeplitz operators

100%
Roch S.
Concrete Operators
|
2015
|
tom 2
|
nr 1
EN
We describe the C*-algebra associated with the finite sections discretization of truncated Toeplitz operators on the model space K2u where u is an infinite Blaschke product. As consequences, we get a stability criterion for the finite sections discretization and results on spectral and pseudospectral approximation.
3
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Continuity of generalized inverses in Banach algebras

63%
Roch S., Silbermann B.
Studia Mathematica
|
1999
|
tom 136
|
nr 3
197-227
EN
The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.
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