On the inverse-closedness of operator-valued matrices with polynomial off-diagonal decay

2025/01/16 by Lukas Köhldorfer, Köhldorfer, Lukas, Péter Balázs +1 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2501.09603

openalex publication_date 2025/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We give a self-contained proof of a recently established B(H)-valued version of Jaffards Lemma. That is, we show that the Jaffard algebra of B(H)-valued matrices, whose operator norms of their respective entries decay polynomially off the diagonal, is a Banach algebra which is inverse-closed in the Banach algebra B(ℓ²(X;H)) of all bounded linear operators on ℓ²(X;H), the Bochner-space of square-summable H-valued sequences.

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