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Absolutely Summing Morphisms between Hilbert C*-Modules and Modular Pietsch Factorization Problem
Version 1
: Received: 6 February 2023 / Approved: 8 February 2023 / Online: 8 February 2023 (10:58:34 CET)
How to cite: KRISHNA, K. M. Absolutely Summing Morphisms between Hilbert C*-Modules and Modular Pietsch Factorization Problem. Preprints 2023, 2023020146. https://doi.org/10.20944/preprints202302.0146.v1 KRISHNA, K. M. Absolutely Summing Morphisms between Hilbert C*-Modules and Modular Pietsch Factorization Problem. Preprints 2023, 2023020146. https://doi.org/10.20944/preprints202302.0146.v1
Abstract
Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom [J. Funct. Anal., 2021], we introduce the notion of p-absolutely summing morphisms between Hilbert C*-modules over commutative C*-algebras. We show that an adjointable morphism between Hilbert C*-modules over monotone closed commutative C*-algebra is 2-absolutely summing if and only if it is Hilbert-Schmidt. We formulate version of Pietsch factorization problem for p-absolutely summing morphisms and solve partially.
Keywords
Absolutely summing operator; Commutative C*-algebra; Hilbert C*-module; Hilbert-Schmidt operator
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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