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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
Posted:
July 7, 2005
MathSciNet review:
2176016
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Abstract |
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Abstract: The operator spaces  ,  , generalizing the row and column Hilbert spaces, and arising in the authors' previous study of contractively complemented subspaces of  -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  to a row or column space is explicitly calculated.
References
- 1.
Jonathan Arazy and Yaakov Friedman, Contractive projections in
 and  , Mem. Amer. Math. Soc. 13 (1978), no 200. MR 0481219 (82b:47023)
- 2.
David P. Blecher and Christian Le Merdy, Operator algebras and their modules--an operator space approach, Clarendon Press, Oxford, 2004. MR 2111973
- 3.
Edward Effros and Zhong-Jin Ruan, Operator Spaces, Oxford University Press, 2000. MR 1793753 (2002a:46082)
- 4.
Yaakov Friedman and Bernard Russo, Solution of the contractive projection problem, J. Funct. Anal. 60 (1985), 56-79. MR 0780104 (87a:46115)
- 5.
Richard V. Kadison and John R. Ringrose, Fundamentals of the Theory of Operator Algebras, Volume II, Academic Press, 1986. MR 0859186 (88d:46106)
- 6.
Ben Mathes, Characterizations of row and column Hilbert space, J. London Math. Soc. (2) 50 (1994), 199-208. MR 1277763 (96b:47048)
- 7.
Matthew Neal and Bernard Russo, Contractive projections and operator spaces, Trans. Amer. Math. Soc. 355 (2003), 2223-2362. MR 1973989 (2004c:46117)
- 8.
Vern Paulsen, Completely bounded maps and operator algebras, Cambridge Studies in Advanced Mathematics 78, Cambridge University Press, Cambridge, 2002. MR 1976867 (2004c:46118)
- 9.
Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, 2003. MR 2006539 (2004k:46097)
- 10.
A. Guyan Robertson, Injective matricial Hilbert spaces, Math. Proc. Cambridge Philos. Soc. 110 (1991), 183-190. MR 1104613 (93d:46101)
- 11.
Takeo Yokonuma, Tensor spaces and exterior algebra, Translations of Mathematical Monographs, Volume 108, American Mathematical Society, 1992. MR 1187759 (93j:15020)
- 12.
Chun Zhang, Completely bounded Banach-Mazur distance, Proc. Edinburgh Math. Soc. 40 (1997), 247-260. MR 1454020 (98e:46021)
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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
Posted:
July 7, 2005
Communicated by:
David R. Larson
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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