On the proximinality of compact operators with range in $C(S)$
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- by Jaroslav Mach PDF
- Proc. Amer. Math. Soc. 72 (1978), 99-104 Request permission
Abstract:
It is proved that the space of compact operators on X into $C(S)$ is proximinal in the corresponding space of bounded operators, if X is a Hilbert space, a space ${l_p},1 < p < + \infty$, or the space ${c_0}$.References
-
N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
- Richard B. Holmes and Bernard R. Kripke, Best approximation by compact operators, Indiana Univ. Math. J. 21 (1971/72), 255–263. MR 296659, DOI 10.1512/iumj.1971.21.21020
- Richard Holmes, Bruce Scranton, and Joseph Ward, Best approximation by compact operators. II, Bull. Amer. Math. Soc. 80 (1974), 98–102. MR 355663, DOI 10.1090/S0002-9904-1974-13370-7
- Richard Holmes, Bruce Scranton, and Joseph Ward, Approximation from the space of compact operators and other $M$-ideals, Duke Math. J. 42 (1975), 259–269. MR 394301
- Richard B. Holmes, Bruce E. Scranton, and Joseph D. Ward, Uniqueness of commuting compact approximations, Trans. Amer. Math. Soc. 208 (1975), 330–340. MR 380480, DOI 10.1090/S0002-9947-1975-0380480-0 G. Köthe, Topologische lineare Räume. I, Springer-Verlag, Berlin and New York, 1966.
- Ernest Michael, Continuous selections. I, Ann. of Math. (2) 63 (1956), 361–382. MR 77107, DOI 10.2307/1969615
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 99-104
- MSC: Primary 47B05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0512853-5
- MathSciNet review: 0512853