A property of compact operators
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- by Herbert Kamowitz PDF
- Proc. Amer. Math. Soc. 91 (1984), 231-236 Request permission
Abstract:
In this note it is shown that if $T$ is a compact linear operator on a wide class of Banach spaces of the form $C(S)$, compact $S$, or ${L^1}(S,\Sigma ,\mu )$, then $\left \| {I + T} \right \| = 1 + \left \| T \right \|$. This generalizes similar theorems for the spaces $C\left [ {0,1} \right ]$ and ${L^1}(0,1)$.References
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- I. K. Daugavet, A property of completely continuous operators in the space $C$, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 157–158 (Russian). MR 0157225 N. Dunford and J. T. Schwartz, Linear operators. Part I, Interscience, New York, 1958. C. A. Hayes and C. Y. Pauc, Derivation and martingales, Springer-Verlag, Berlin and New York, 1970.
- G. E. Shilov and B. L. Gurevich, Integral, measure and derivative: A unified approach, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. Revised English edition, translated from the Russian and edited by Richard A. Silverman. MR 0194571
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 231-236
- MSC: Primary 47B38; Secondary 46E99
- DOI: https://doi.org/10.1090/S0002-9939-1984-0740177-2
- MathSciNet review: 740177