Noncoincidence of the strict and strong operator topologies
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- by Joel H. Shapiro PDF
- Proc. Amer. Math. Soc. 35 (1972), 81-87 Request permission
Abstract:
Let E be an infinite-dimensional linear subspace of $C(S)$, the space of bounded continuous functions on a locally compact Hausdorff space S. If $\mu$ is a regular Borel measure on S, then each element of E may be regarded as a multiplication operator on ${L^p}(\mu )(1 \leqq p < \infty )$. Our main result is that the strong operator topology this identification induces on E is properly weaker than the strict topology. For E the space of bounded analytic functions on a plane region G, and $\mu$ Lebesgue measure on G, this answers negatively a question raised by Rubel and Shields in [9]. In addition, our methods provide information about the absolutely p-summing properties of the strict topology on subspaces of $C(S)$, and the bounded weak star topology on conjugate Banach spaces.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 81-87
- MSC: Primary 46E10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0306878-7
- MathSciNet review: 0306878