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

TL;DR

This paper extends the concept of absolutely summing morphisms to Hilbert C*-modules over commutative C*-algebras, establishing a characterization of 2-absolutely summing morphisms as Hilbert-Schmidt and addressing a Pietsch factorization problem.

Contribution

It introduces p-absolutely summing morphisms for Hilbert C*-modules and characterizes 2-absolutely summing morphisms as Hilbert-Schmidt, advancing the understanding of operator ideals in this context.

Findings

2-absolutely summing morphisms are equivalent to Hilbert-Schmidt operators.

Partial solutions to the Pietsch factorization problem for these morphisms.

Extension of summing operator theory to Hilbert C*-modules over commutative algebras.

Abstract

Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom \textit{[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