Infinite matrices and invariant means

Author:
Paul Schaefer

Journal:
Proc. Amer. Math. Soc. **36** (1972), 104-110

MSC:
Primary 40C05

DOI:
https://doi.org/10.1090/S0002-9939-1972-0306763-0

MathSciNet review:
0306763

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a one-to-one mapping of the set of positive integers into itself such that for all positive integers *n* and *p*, where . A continuous linear functional on the space of real bounded sequences is an invariant mean if when the sequence has for all *n*, , and for all bounded sequences *x*. Let be the set of bounded sequences all of whose invariant means are equal. If is a real infinite matrix, then *A* is said to be (1) -conservative if for all convergent sequences *x*, (2) -regular if and for all convergent sequences *x* and all invariant means , and (3) -coercive if for all bounded sequences *x*. Necessary and sufficient conditions are obtained to characterize these classes of matrices.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0306763-0

Keywords:
-conservative matrices,
-regular matrices,
-coercive matrices,
invariant means,
almost convergence

Article copyright:
© Copyright 1972
American Mathematical Society