%0 Electronic Article %A Conway, John B. %I American Mathematical Society (AMS) %D 1975 %D 1975 %G English %@ 0002-9947 %@ 1088-6850 %~ Universitätsbibliothek "Georgius Agricola" %T On the Calkin algebra and the covering homotopy property %V 211 %J Transactions of the American Mathematical Society %V 211 %P 135-142 %U http://dx.doi.org/10.1090/s0002-9947-1975-0399875-4 %X

Let H \mathcal {H} be a separable Hilbert space, B ( H ) \mathcal {B}(\mathcal {H}) the bounded operators on H , K \mathcal {H},\mathcal {K} the ideal of compact operators, and π \pi the natural map from B ( H ) \mathcal {B}(\mathcal {H}) onto the Calkin algebra B ( H ) / K \mathcal {B}(\mathcal {H})/\mathcal {K} . Suppose X is a compact metric space and Φ : C ( X ) × [ 0 , 1 ] B ( H ) / K \Phi :C(X) \times [0,1] \to \mathcal {B}(\mathcal {H})/\mathcal {K} is a continuous function such that Φ ( , t ) \Phi ( \cdot ,t) is a \ast -isomorphism for each t and such that there is a \ast -isomorphism ψ : C ( X ) B ( H ) \psi :C(X) \to \mathcal {B}(\mathcal {H}) with π ψ ( ) = Φ ( , 0 ) \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 Ψ : C ( X ) × [ 0 , 1 ] B ( H ) \Psi :C(X) \times [0,1] \to \mathcal {B}(\mathcal {H}) such that π Ψ = Φ \pi \Psi = \Phi and Ψ ( , 0 ) = ψ ( ) \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.

%Z https://katalog.ub.tu-freiberg.de/Record/ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTA5MC9zMDAwMi05OTQ3LTE5NzUtMDM5OTg3NS00 %U https://katalog.ub.tu-freiberg.de/Record/ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTA5MC9zMDAwMi05OTQ3LTE5NzUtMDM5OTg3NS00