Quasi *-algebras of measurable operators

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Abstract

Non-commutative Lp-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p 2 they are also proved to possess a su cient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a nite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (X;A0) possessing a su cient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.
Lingua originaleEnglish
pagine (da-a)289-305
Numero di pagine17
RivistaStudia Mathematica
Volume172
Stato di pubblicazionePublished - 2006

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Sesquilinear form
Algebra
Operator
Noncommutative Lp-spaces
Abstract algebra
Von Neumann Algebra
Invariance
Class
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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abstract = "Non-commutative Lp-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p 2 they are also proved to possess a su cient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a nite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (X;A0) possessing a su cient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.",
author = "Camillo Trapani and Fabio Bagarello and Salvatore Triolo",
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journal = "Studia Mathematica",
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T1 - Quasi *-algebras of measurable operators

AU - Trapani, Camillo

AU - Bagarello, Fabio

AU - Triolo, Salvatore

PY - 2006

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N2 - Non-commutative Lp-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p 2 they are also proved to possess a su cient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a nite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (X;A0) possessing a su cient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.

AB - Non-commutative Lp-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p 2 they are also proved to possess a su cient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a nite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (X;A0) possessing a su cient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.

UR - http://hdl.handle.net/10447/14890

UR - https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/172/3/89798/quasi-algebras-of-measurable-operators

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EP - 305

JO - Studia Mathematica

JF - Studia Mathematica

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