Norm reduction of averaging operators
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- by H. B. Cohen, M. A. Labbe and J. Wolfe PDF
- Proc. Amer. Math. Soc. 35 (1972), 519-523 Request permission
Abstract:
Suppose $\phi :S \to T$ is an irreducible map of compact Hausdorff spaces, and $\mu :T \to M(S)$ the integral representation of an averaging operator for $\phi$. We obtain an inequality of the form $\left \| {\mu (t)} \right \| \leqq \left \| \mu \right \| - a(t)$, where $a(t){\text {is}}$ a positive number depending on t. From this, some results of Amir and Isbell-Semadeni on ${P_\lambda }$ spaces are shown to follow quickly and a theorem on the isomorphism of certain continuous function spaces is derived.References
- D. Amir, Continuous functions’ spaces with the bounded extension property, Bull. Res. Council Israel Sect. F 10F (1962), 133–138 (1962). MR 143026
- D. Amir, Projections onto continuous function spaces, Proc. Amer. Math. Soc. 15 (1964), 396–402. MR 165350, DOI 10.1090/S0002-9939-1964-0165350-3
- J. R. Isbell and Z. Semadeni, Projection constants and spaces of continuous functions, Trans. Amer. Math. Soc. 107 (1963), 38–48. MR 146649, DOI 10.1090/S0002-9947-1963-0146649-7
- A. Pełczyński, Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math. (Rozprawy Mat.) 58 (1968), 92. MR 227751 J. Wolfe, Injective Banach spaces of the type $C(T)$, Doctoral Dissertation, University of California, Berkeley, Calif., 1971.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 519-523
- MSC: Primary 46E15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0324389-X
- MathSciNet review: 0324389