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Geometric characterizations of some classes of operators in C*-algebras and von Neumann algebras

Author(s): Charles Akemann; Nik Weaver
Journal: Proc. Amer. Math. Soc. 130 (2002), 3033-3037.
MSC (2000): Primary 46L05; Secondary 47A05, 46B04, 46B20
Posted: May 8, 2002
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Abstract: We present geometric characterizations of the partial isometries, unitaries, and invertible operators in C*-algebras and von Neumann algebras.

References:

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D. P. Blecher, E. G. Effros, and V. Zarikian, One-sided $M$-ideals and multipliers in operator spaces, I, manuscript.

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R. V. Kadison, Isometries of operator algebras, Ann. of Math. 54 (1951), 325-338. MR 13:256a

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R. V. Kadison and J. Ringrose, Fundamentals of the theory of operator algebras, Volume II, Academic Press, New York, 1986. MR 88d:46106

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G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29-43. MR 24:A2860

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N. C. Phillips, Continuous-trace C*-algebras not isomorphic to their opposite algebras, Internat. J. Math. 12 (2001), 263-275.

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A. L. Paterson and A. M. Sinclair, Characterization of isometries between C*-algebras, J. London Math. Soc. (2) 5 (1972), 755-761. MR 48:2783

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M. Takesaki, Theory of operator algebras I, Springer-Verlag, New York, 1979. MR 81e:46038

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Additional Information:

Charles Akemann
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: akemann@math.ucsb.edu

Nik Weaver
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
Email: nweaver@math.wustl.edu

DOI: 10.1090/S0002-9939-02-06643-1
PII: S 0002-9939(02)06643-1
Received by editor(s): May 24, 2001
Posted: May 8, 2002
Additional Notes: The second author was supported by NSF grant DMS-0070634
Dedicated: Dedicated to Richard V. Kadison on his 75th birthday
Communicated by: David R. Larson
Copyright of article: Copyright 2002, American Mathematical Society

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