Absolutely Summing Morphisms between Hilbert C*-Modules and Modular Pietsch Factorization Problem

K. MAHESH KRISHNA

doi:10.20944/preprints202302.0146.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 6 February 2023 / Approved: 8 February 2023 / Online: 8 February 2023 (10:58:34 CET)

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.

Absolutely summing operator; Commutative C*-algebra; Hilbert C*-module; Hilbert-Schmidt operator

Computer Science and Mathematics, Analysis

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Absolutely Summing Morphisms between Hilbert C*-Modules and Modular Pietsch Factorization Problem

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