Enveloping norms of regularly P-operators in Banach lattices

Alpay S., Emelyanov E., Gorokhova S.

Positivity, vol.28, no.3, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.1007/s11117-024-01055-2
  • Journal Name: Positivity
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Business Source Elite, Business Source Premier, MathSciNet, zbMATH
  • Keywords: 46B25, 46B42, 46B50, 47B60, Banach lattice, Enveloping norm, Operator linear class, Regularly P-operator
  • Middle East Technical University Affiliated: Yes

Abstract

The span of positive linear operators belonging to an operator linear class P and acting between Banach lattices is rarely a Banach space under the operator norm. We investigate the enveloping norm ‖S‖r-P=inf{‖T‖:±S≤T∈P} on span(P+(E,F)) that is complete under rather mild assumptions on P.