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- Title
Strong completeness of a class of L^2(T)-type Riesz spaces.
- Authors
Kalauch, Anke; Kuo, Wen-Chi; Watson, Bruce A.
- Abstract
The L^{p}, 1\le p\le \infty, spaces have been generalized to the setting of Riesz spaces as {L}^{p}(T) spaces, on which there are R(T)-valued norms. The strong sequential completeness of the space {L}^{1}(T) and the strong completeness of {L}^{\infty }(T) with resepct to their respective R(T)-valued norms were established by Kuo, Rodda, and Watson. In the current work, the T-strong completeness of {L}^{2}(T) is established via the Riesz–Fischer type theorem given by Kalauch, Kuo, and Watson. It is also shown that the conditional expectation operator T is a weak order unit for the T-strong dual.
- Subjects
RIESZ spaces; CONDITIONAL expectations
- Publication
Proceedings of the American Mathematical Society, Series B, 2024, Vol 11, p243
- ISSN
2330-1511
- Publication type
Article
- DOI
10.1090/bproc/230