Wiener pairs of Banach algebras of operator-valued matrices
Lukas K\"ohldorfer, Peter Balazs

TL;DR
This paper introduces new classes of operator-valued matrix Banach algebras, demonstrating their inverse-closedness and symmetry within the algebra of bounded operators on Hilbert space-valued sequence spaces.
Contribution
It constructs several novel examples of Wiener pairs of Banach algebras of operator-valued matrices and proves their inverse-closedness and symmetry properties.
Findings
New operator-valued matrix Banach algebras are inverse-closed in bounded operators.
These algebras are shown to be symmetric.
The paper generalizes classical decay conditions to operator-valued settings.
Abstract
In this article we introduce several new examples of Wiener pairs , where is the Banach algebra of bounded operators acting on the Hilbert space-valued Bochner sequence space and is a Banach algebra consisting of operator-valued matrices indexed by some relatively separated set . In particular, we introduce -valued versions of the Jaffard algebra, of certain weighted Schur-type algebras, of Banach algebras which are defined by more general off-diagonal decay conditions than polynomial decay, of weighted versions of the Baskakov-Gohberg-Sj\"ostrand algebra, and of anisotropic variations of all of these matrix algebras, and show that they are inverse-closed in . In…
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Taxonomy
TopicsMatrix Theory and Algorithms · advanced mathematical theories · Algebraic and Geometric Analysis
