The Twisted Hilbert Space Ideals
F\'elix Cabello S\'anchez, Ricardo Garc\'ia
TL;DR
This paper investigates operators on Hilbert spaces that can be extended or lifted to twisted Hilbert spaces, characterizing their structure and identifying their inclusion of Schatten classes and specific multiplication operators.
Contribution
It introduces a new class of operators that form an ideal containing Schatten classes and characterizes liftable/extensible multiplication operators on lexp spaces.
Findings
Operators form an ideal containing all Schatten classes.
Characterization of liftable/extensible multiplication operators on lexp.
Identification of conditions for operators to extend to twisted Hilbert spaces.
Abstract
We study those operators on a Hilbert space that can be lifted / extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators on that are liftable / extensible through centralizers.
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