Weak generalized limit and ergodic theorems (Q2754853)
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scientific article; zbMATH DE number 1668471
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak generalized limit and ergodic theorems |
scientific article; zbMATH DE number 1668471 |
Statements
4 November 2001
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Banach limit
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semigroup of operators
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operator means
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ergodic theorem
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linear relation
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integral means of a \(C_0\)-semigroup
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Weak generalized limit and ergodic theorems (English)
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The authors extend the notion of the Banach generalized limit to bounded generalized sequences (functions on a directed set) with values in a Banach space \(X\). This is used to weaken the assumptions in several well known results of operator theory including the decomposition of a linear relation on a Banach space, conditions for the uniform convergence of operator means, the strong convergence of the integral means of a \(C_0\)-semigroup. For the latter problem necessary and sufficient conditions are given. Note that a different criterion was given by \textit{J. A. Goldstein} [``Semigroups of Linear Operators and Applications'', Oxford University Press (1985; Zbl 0592.47034)].
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