Hyperreflexivity of the space of module homomorphisms between non-commutative Lp-spaces

Let M be a von Neumann algebra, and let 0<p,q≤∞. Then the space HomM(Lp(M),Lq(M)) of all right M-module homomorphisms from Lp(M) to Lq(M) is a reflexive subspace of the space of all continuous linear maps from Lp(M) to Lq(M). Further, the space HomM(Lp(M),Lq(M)) is hyperreflexive in each of the f...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 498; no. 2
Main Authors Alaminos, J., Extremera, J., Godoy, M.L.C., Villena, A.R.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2021
Subjects
Hyperreflexive subspaces
Injective von Neumann algebras
Module homomorphisms
Non-commutative [formula omitted]-spaces
Reflexive subspaces
Reflexive subspaces
Module homomorphisms
Injective von Neumann algebras
Non-commutative Lp-spaces
Hyperreflexive subspaces
Online AccessGet full text

Cover

More Information
Summary:Let M be a von Neumann algebra, and let 0<p,q≤∞. Then the space HomM(Lp(M),Lq(M)) of all right M-module homomorphisms from Lp(M) to Lq(M) is a reflexive subspace of the space of all continuous linear maps from Lp(M) to Lq(M). Further, the space HomM(Lp(M),Lq(M)) is hyperreflexive in each of the following cases: (i) 1≤q<p≤∞; (ii) 1≤p,q≤∞ and M is injective, in which case the hyperreflexivity constant is at most 8.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.124964