Compact covariance operators
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- by Charles R. Baker and Ian W. McKeague PDF
- Proc. Amer. Math. Soc. 83 (1981), 590-593 Request permission
Abstract:
Let $B$ be a real separable Banach space and $R:{B^*} \to B$ a covariance operator. All representations of $R$ in the form $\sum {e_n} \otimes {e_n}$, $\{ {e_n},n \geqslant 1\} \subset B$, are characterized. Necessary and sufficient conditions for $R$ to be compact are obtained, including a generalization of Mercer’s theorem. An application to characteristic functions is given.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 590-593
- MSC: Primary 47B05; Secondary 47B15, 60B11
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627699-7
- MathSciNet review: 627699