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

2022/12/01 by Alpay, Safak, Emelyanov, Eduard, Gorokhova, Svetlana
#46B25 #46B42 #46B50 #47B60 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2212.00441

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.

Related

• Regularly limited, Grothendieck, and Dunford--Pettis operators
• Operators Affiliated to Banach Lattice Properties and the Enveloping Norms
• Algebras of Lebesgue and KB regular operators in Banach lattices
• (p,q)-regular operators between Banach lattices
• Contribution to operators between Banach lattices