Enveloping norms on the spaces of regularly P-operators in Banach lattices

TL;DR

This paper introduces and analyzes the enveloping norms of regularly P-operators between Banach lattices, establishing conditions for these operators to form Banach spaces and lattices under the enveloping norm.

Contribution

It defines and studies the properties of enveloping norms for regularly P-operators, providing new conditions for their structure as Banach spaces and lattices.

Findings

Regularly P-operators form a Banach space under the enveloping norm if P is closed in L(E,F).

Conditions are given for regularly P-operators to form a Banach lattice.

The paper extends the theory of operator norms in Banach lattices.

Abstract

We introduce and study the enveloping norms of regularly P-operators between Banach lattices E and F, where P is a subspace of the space L(E,F) of continuous operators from E to F. We prove that if P is closed in L(E,F) in the operator norm then the regularly P-operators forms a Banach space under the enveloping norm. Conditions providing that regularly P-operators forms a Banach lattice under the enveloping norm are given.