On the multiplicative behavior of regular matrices
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- by Robert E. Atalla PDF
- Proc. Amer. Math. Soc. 26 (1970), 437-446 Request permission
Addendum: Proc. Amer. Math. Soc. 48 (1975), 268.
Abstract:
Let $T$ be a bounded linear operator on $C(X),X$ compact ${T_2}$, with $T1 = 1$. We define ${M_T}$ to be the subalgebra of $C(X)$ consisting of $g$ such that $T(fg) = TfTg$ for all $f$, and give a characterization of ${M_T}$. We apply the characterization to the multiplicative behavior of regular matrices, considering these as linear operators on $C(\beta N\backslash N)$. We also relate invariance properties of a matrix under suitable mappings of the integers to topological properties of its support set in $\beta N\backslash N$, and give an example of a nonnegative multiplicative matrix whose support set is nowhere dense in $\beta N\backslash N$.References
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Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 26 (1970), 437-446
- MSC: Primary 47.25; Secondary 40.00
- DOI: https://doi.org/10.1090/S0002-9939-1970-0271752-X
- MathSciNet review: 0271752