Abstract
We characterize the Schur multipliers of scalar type acting on scattered classes of infinite matrices.
Highlights
This concept was used in different areas of analysis as complex function theory, Banach spaces, operator theory, and multivariate analysis
Journal of Function Spaces and Applications. In his paper it is proved a theorem about Schur multipliers which are Toeplitz matrices, that is about the matrices of the form
It is well known that M 2 coincides with S1, S1, the space of all Schur multipliers from S1 into S1, see, for example, 4
Summary
In 5 , Aleksandrov and Peller characterized the Toeplitz matrices which are Schur multipliers for Sp, 0 < p < 1 The space pms endowed with the norm b with respect to the usual product of sequences. A set of sufficient conditions in order for a matrix of the type α to be a Schur multiplier is given in 6 , namely, the following theorem was proved. It is well known that M 2 coincides with S1, S1 , the space of all Schur multipliers from S1 into S1, see, for example, 4 Using this fact we give a simpler proof of the first statement of Corollary 1. Let A α ⊗ β with α αn n≥1 ∈ 2 and β βn n≥1 ∈ 2
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