 

Michael Frank, Vladimir Manuilov, and Evgenij Troitsky
A reflexivity criterion for Hilbert C*modules over commutative C*algebras view print


Published: 
November 12, 2010 
Keywords: 
Hilbert C*module; reflexivity; commutative C*algebra 
Subject: 
Primary 46L08, Secondary 54D99 


Abstract
A C*algebra A is C*reflexive if any countably generated
Hilbert C*module M over A is C*reflexive, i.e., the
second dual module M'' coincides with M. We show that a
commutative C*algebra A is C*reflexive if and only if
for any sequence I_{k} of mutually orthogonal nonzero C*subalgebras, the
canonical inclusion ⊕_{k} I_{k}⊂ A doesn't extend to an
inclusion of ∏_{k} I_{k}.


Acknowledgements
This work is a part of the joint DFGRFBR project (RFBR grant 070191555 / DFG project "KTheory, C*Algebras, and Index Theory''). The second and the third named authors acknowledge also partial support from RFBR grant 080100034


Author information
Michael Frank:
HTWK Leipzig, FB IMN, Postfach 301166, D04251 Leipzig, Germany
mfrank@imn.htwkleipzig.de
Vladimir Manuilov:
Dept. of Mech. and Math., Moscow State University, 119991 GSP1 Moscow, Russia and Harbin Institute of Technology, Harbin, P. R. China
manuilov@mech.math.msu.su
Evgenij Troitsky:
Dept. of Mech. and Math., Moscow State University, 119991 GSP1 Moscow, Russia
troitsky@mech.math.msu.su

