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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Representation of contractively complemented Hilbertian operator spaces on the Fock space


Authors: Matthew Neal and Bernard Russo
Journal: Proc. Amer. Math. Soc. 134 (2006), 475-485
MSC (2000): Primary 46L07
Published electronically: July 7, 2005
MathSciNet review: 2176016
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Abstract: The operator spaces $H_n^k$, $1\le k\le n$, generalizing the row and column Hilbert spaces, and arising in the authors' previous study of contractively complemented subspaces of $C^*$-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. The completely bounded Banach-Mazur distance from $H_n^k$ to a row or column space is explicitly calculated.


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Additional Information

Matthew Neal
Affiliation: Department of Mathematics and Computer Science, Denison University, Granville, Ohio 43023
Email: nealm@denison.edu

Bernard Russo
Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875
Email: brusso@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08130-X
PII: S 0002-9939(05)08130-X
Keywords: Hilbertian operator space, homogeneous operator space, contractive projection, creation operator, anti-symmetric Fock space, completely bounded Banach-Mazur distance
Received by editor(s): September 22, 2004
Published electronically: July 7, 2005
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.