The maximal C*-algebra of quotients as an operator bimodule

Pere Ara; Martin Mathieu; Eduard Ortega

doi:https://doi.org/10.1007/s00013-009-2944-5

The maximal C*-algebra of quotients as an operator bimodule

Pere Ara, Martin Mathieu, Eduard Ortega

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Abstract

We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product A ⊗h labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved. © 2009 Birkhäuser Verlag Basel/Switzerland.

Original language	English
Pages (from-to)	405-413
Journal	Archiv der Mathematik
Volume	92
DOIs	https://doi.org/10.1007/s00013-009-2944-5
Publication status	Published - 1 Jan 2009

Keywords

Completely bounded module homomorphisms
Haagerup tensor product
Local multiplier algebra
Maximal C*-algebra of quotients
Strong Morita equivalence

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abstract = "We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product A ⊗h labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved. {\textcopyright} 2009 Birkh{\"a}user Verlag Basel/Switzerland.",

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AU - Mathieu, Martin

AU - Ortega, Eduard

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N2 - We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product A ⊗h labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved. © 2009 Birkhäuser Verlag Basel/Switzerland.

AB - We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product A ⊗h labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved. © 2009 Birkhäuser Verlag Basel/Switzerland.

KW - Completely bounded module homomorphisms

KW - Haagerup tensor product

KW - Local multiplier algebra

KW - Maximal C-algebra of quotients

KW - Strong Morita equivalence

U2 - https://doi.org/10.1007/s00013-009-2944-5

DO - https://doi.org/10.1007/s00013-009-2944-5

M3 - Article

SN - 0003-889X

VL - 92

SP - 405

EP - 413

JO - Archiv der Mathematik

JF - Archiv der Mathematik

ER -

The maximal C*-algebra of quotients as an operator bimodule

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Keywords

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