TY - JOUR
T1 - The maximal C*-algebra of quotients as an operator bimodule
AU - Ara, Pere
AU - Mathieu, Martin
AU - Ortega, Eduard
PY - 2009/1/1
Y1 - 2009/1/1
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 - Haagerup tensor product
KW - Completely bounded module homomorphisms
KW - Strong Morita equivalence
KW - Maximal C-algebra of quotients
KW - Local multiplier algebra
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=3118466
U2 - 10.1007/s00013-009-2944-5
DO - 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 -