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- W1970612462 abstract "Let $mathcal {H}$ be a separable Hilbert space, $mathcal {B}(mathcal {H})$ the bounded operators on $mathcal {H},mathcal {K}$ the ideal of compact operators, and $pi$ the natural map from $mathcal {B}(mathcal {H})$ onto the Calkin algebra $mathcal {B}(mathcal {H})/mathcal {K}$. Suppose X is a compact metric space and $Phi :C(X) times [0,1] to mathcal {B}(mathcal {H})/mathcal {K}$ is a continuous function such that $Phi ( cdot ,t)$ is a $ast$-isomorphism for each t and such that there is a $ast$-isomorphism $psi :C(X) to mathcal {B}(mathcal {H})$ with $pi psi ( cdot ) = Phi ( cdot ,0)$. 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 $Psi :C(X) times [0,1] to mathcal {B}(mathcal {H})$ such that $pi Psi = Phi$ and $Psi ( cdot ,0) = psi ( cdot )$. Furthermore if X is the disjoint union of two spaces that both have this property, then X itself has this property." @default.
- W1970612462 created "2016-06-24" @default.
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- W1970612462 date "1975-01-01" @default.
- W1970612462 modified "2023-09-24" @default.
- W1970612462 title "On the Calkin algebra and the covering homotopy property" @default.
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- W1970612462 doi "https://doi.org/10.1090/s0002-9947-1975-0399875-4" @default.
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