On the Calkin algebra and the covering homotopy property
Author:
John B. Conway
Journal:
Trans. Amer. Math. Soc. 211 (1975), 135142
MSC:
Primary 46L05; Secondary 46M20, 55F05, 58G10
MathSciNet review:
0399875
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Abstract: Let be a separable Hilbert space, the bounded operators on the ideal of compact operators, and the natural map from onto the Calkin algebra . Suppose X is a compact metric space and is a continuous function such that is a isomorphism for each t and such that there is a isomorphism with . It is shown in this paper that if X is a simple Jordan curve, a simple closed Jordan curve, or a totally disconnected metric space then there is a continuous map such that and . Furthermore if X is the disjoint union of two spaces that both have this property, then X itself has this property.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197503998754
PII:
S 00029947(1975)03998754
Keywords:
Operators on a Hilbert space,
Calkin algebra,
covering homotopy property
Article copyright:
© Copyright 1975 American Mathematical Society
