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.
 [1]
Huzihiro
Araki, Misoo
Bae Smith, and Larry
Smith, On the homotopical significance of the type of von Neumann
algebra factors, Comm. Math. Phys. 22 (1971),
71–88. MR
0288587 (44 #5783)
 [2]
Lawrence
G. Brown, Operator algebras and algebraic
𝐾theory, Bull. Amer. Math. Soc.
81 (1975), no. 6,
1119–1121. MR 0383090
(52 #3971), http://dx.doi.org/10.1090/S000299041975139437
 [3]
L.
G. Brown, R.
G. Douglas, and P.
A. Fillmore, Extensions of 𝐶*algebras,
operators with compact selfcommutators, and 𝐾homology,
Bull. Amer. Math. Soc. 79 (1973), 973–978. MR 0346540
(49 #11265), http://dx.doi.org/10.1090/S000299041973132847
 [4]
L.
G. Brown, R.
G. Douglas, and P.
A. Fillmore, Unitary equivalence modulo the compact operators and
extensions of 𝐶*algebras, Proceedings of a Conference on
Operator Theory (Dalhousie Univ., Halifax, N.S., 1973) Springer, Berlin,
1973, pp. 58–128. Lecture Notes in Math., Vol. 345. MR 0380478
(52 #1378)
 [5]
Paul
R. Halmos, A Hilbert space problem book, D. Van Nostrand Co.,
Inc., Princeton, N.J.Toronto, Ont.London, 1967. MR 0208368
(34 #8178)
 [6]
Jerome
Kaminker and Claude
Schochet, 𝐸𝑥𝑡(𝑋) from a homological
point of view, Proceedings Conference Operator Theory (Dalhousie
Univ., Halifax, N. S., 1973) Springer, Berlin, 1973,
pp. 129–140. Lecture Notes in Math., Vol. 345. MR 0448119
(56 #6429)
 [7]
Ernest
Michael, Continuous selections. I, Ann. of Math. (2)
63 (1956), 361–382. MR 0077107
(17,990e)
 [8]
Frigyes
Riesz and Béla
Sz.Nagy, Functional analysis, Frederick Ungar Publishing Co.,
New York, 1955. Translated by Leo F. Boron. MR 0071727
(17,175i)
 [1]
 H. Araki, M.S. B. Smith and L. Smith, On the homotopical significance of the type of von Neumann algebra factors, Comm. Math. Phys. 22 (1971), 7188. MR 44 #5783. MR 0288587 (44:5783)
 [2]
 L. G. Brown, Operator algebras and algebraic Ktheory (to appear). MR 0383090 (52:3971)
 [3]
 L. G. Brown, R. G. Douglas and P. A. Fillmore, Extensions of algebras, operators with compact selfcommutators, and Khomology, Bull. Amer. Math. Soc. 79 (1973), 973978. MR 0346540 (49:11265)
 [4]
 , Unitary equivalence modulo the compact opertors and extensions of algebras, Proc. Conf. on Operator Theory, Lecture Notes in Math., vol. 345, SpringerVerlag, New York, 1973, pp. 58128. MR 0380478 (52:1378)
 [5]
 P. R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N. J., 1967. MR 34 #8178. MR 0208368 (34:8178)
 [6]
 J. Kaminker and C. Schochet, from a homological point of view, Proc. Conf. on Operator Theory, Lecture Notes in Math., vol. 345, SpringerVerlag, New York, 1973, pp. 129140. MR 0448119 (56:6429)
 [7]
 E. Michael, Continuous selections. I, Ann. of Math. (2) 63 (1956), 361382. MR 17, 990. MR 0077107 (17:990e)
 [8]
 F. Riesz and B. Sz.Nagy, Leçons d'analyse fonctionelle, 2nd ed., Akad. Kiadó, Budapest, 1953; English transl., Functional analysis, Ungar, New York, 1955. MR 15, 132; 17, 175. MR 0071727 (17:175i)
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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
