Let M, N, R be W*-algebras, with R unitally embedded in both M and N. By using Reduction Theory, we describe the predual (Mcircle times(R)N), of the W*-tensor product Mcircle times(R)N over the common W*-subalgebra R in the separable predual case. We also analyze the case when R is a direct sum of full matrix algebras, without any separability assumption. In the last situation, the predual (Mcircle times(R)N)(*) is described by the center Z(M-R circle times N (*) (R)) of the R-R bimodule M-R(*) circle times N-* (R). the last one being isomorphic to the predual of M circle times N. It is also shown that such a reduction-free result cannot be extended to the remaining cases. (C) 2003 Elsevier Inc. All rights reserved.

Fidaleo, F. (2004). The predual of W*-tensor products over W*-subalgebras (separable case). JOURNAL OF FUNCTIONAL ANALYSIS [10.1016/j.jfa.2003.06.004].

The predual of W*-tensor products over W*-subalgebras (separable case)

FIDALEO, FRANCESCO
2004

Abstract

Let M, N, R be W*-algebras, with R unitally embedded in both M and N. By using Reduction Theory, we describe the predual (Mcircle times(R)N), of the W*-tensor product Mcircle times(R)N over the common W*-subalgebra R in the separable predual case. We also analyze the case when R is a direct sum of full matrix algebras, without any separability assumption. In the last situation, the predual (Mcircle times(R)N)(*) is described by the center Z(M-R circle times N (*) (R)) of the R-R bimodule M-R(*) circle times N-* (R). the last one being isomorphic to the predual of M circle times N. It is also shown that such a reduction-free result cannot be extended to the remaining cases. (C) 2003 Elsevier Inc. All rights reserved.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
classifications of C*-algebras; factors; operator spaces and completely bounded maps; normed modules and Banach modules; topological modules
Fidaleo, F. (2004). The predual of W*-tensor products over W*-subalgebras (separable case). JOURNAL OF FUNCTIONAL ANALYSIS [10.1016/j.jfa.2003.06.004].
Fidaleo, F
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/31727
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 0
social impact