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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Averaging operators in $C(S)$ and lower semicontinuous sections of continuous maps
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by Seymour Z. Ditor PDF
Trans. Amer. Math. Soc. 175 (1973), 195-208 Request permission

Abstract:

For certain kinds of compact Hausdorff spaces S, necessary and sufficient topological conditions are provided for determining if there exists a norm 1 projection of $C(S)$ onto any given separable selfadjoint subalgebra A, the conditions being in terms of the decomposition that A induces on S. In addition, for arbitrary S and selfadjoint closed subalgebra A of $C(S)$, some results on lower bounds for the norms of projections of $C(S)$ onto A are obtained. An example is given which shows that the greatest lower bound of the projection norms need not be attained.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 175 (1973), 195-208
  • MSC: Primary 46E15; Secondary 46J10, 47B99
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0312228-8
  • MathSciNet review: 0312228