Abel-Schur Multipliers on Banach Spaces of Infinite Matrices

Document Type : Original Article

Author

Nicolae Popa

Institute of Mathematics of Romanian Academy, P.O. BOX 1–764 RO–014700 Bucharest, ROMANIA.

10.22034/kjm.2016.16359

Abstract

We consider a more general class than the class of Schur multipliers namely the Abel-Schur multipliers, which in turn coincide with the bounded linear operators on $\ell_{2}$ preserving the diagonals. We extend to the matrix framework Theorem 2.4 (a) of a paper of Anderson, Clunie, and Pommerenke published in 1974, and as an application of this theorem we obtain a new proof of the necessity of an old theorem of Hardy and Littlewood in 1941.

Keywords

Abel-Schur multipliers

Schur multipliers

Toeplitz matrices

Bloch space of matrices

Subjects

• 15 Linear and multilinear algebra; matrix theory
• 46 Functional analysis
• 47 Operator theory

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