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On a Schur-Type Product for Matrices with Operator Entries

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Abstract

In this paper, we will introduce a new Schur-type product for matrices with operator entries, and explore some of its properties. We shall see a connection between this product and the classical Schur product that will allow us to prove that this set of matrices endowed with such new product defines a Banach algebra. Also, a way to compute the operator and multiplier norms of matrices with operator entries in terms of norms of scalar matrices will be provided. As applications, we present a way to obtain multipliers for one of the products from a multiplier for the other product and show a method to construct a countable amount of elements belonging to different vector measure spaces, from a single element of \(L^\infty (\mathbb {T})\).

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Acknowledgements

The author is thankful to the anonymous reviewers for their comments and suggestions that allowed to improve the paper, and also acknowledges the support provided by MINECO (Spain) under the Project MTM2014-53009-P and by MCIU (Spain) under the Grant FPU14/01032.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Valencia, 46100, Burjassot, Valencia, Spain

    Ismael García-Bayona

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  1. Ismael García-Bayona
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Correspondence to Ismael García-Bayona.

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Communicated by Ali Armandnejad.

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Partially supported by MTM2014-53009-P (MINECO Spain) and FPU14/01032 (MCIU Spain)

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García-Bayona, I. On a Schur-Type Product for Matrices with Operator Entries. Bull. Iran. Math. Soc. 46, 1775–1789 (2020). https://doi.org/10.1007/s41980-020-00358-w

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  • DOI: https://doi.org/10.1007/s41980-020-00358-w

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