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Michael Frank, Vladimir Manuilov, and Evgenij Troitsky
A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras view print
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| Published: |
November 12, 2010 |
| Keywords: |
Hilbert C*-module; reflexivity; commutative C*-algebra |
| Subject: |
Primary 46L08, Secondary 54D99 |
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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 Ik of mutually orthogonal nonzero C*-subalgebras, the
canonical inclusion ⊕k Ik⊂ A doesn't extend to an
inclusion of ∏k Ik.
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| Acknowledgements
This work is a part of the joint DFG-RFBR project (RFBR grant 07-01-91555 / DFG project "K-Theory, C*-Algebras, and Index Theory''). The second and the third named authors acknowledge also partial support from RFBR grant 08-01-00034
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| Author information
Michael Frank:
HTWK Leipzig, FB IMN, Postfach 301166, D-04251 Leipzig, Germany
mfrank@imn.htwk-leipzig.de
Vladimir Manuilov:
Dept. of Mech. and Math., Moscow State University, 119991 GSP-1 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 GSP-1 Moscow, Russia
troitsky@mech.math.msu.su
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