On the Calkin algebra and the covering homotopy property

Author:
John B. Conway

Journal:
Trans. Amer. Math. Soc. **211** (1975), 135-142

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:
https://doi.org/10.1090/S0002-9947-1975-0399875-4

Keywords:
Operators on a Hilbert space,
Calkin algebra,
covering homotopy property

Article copyright:
© Copyright 1975
American Mathematical Society