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• W2113127515 abstract "Connections between (positive) mean ergodic operators acting in Banach lattices and properties of the underlying lattice itself are well understood (see the works of Emel'yanov, Wolff and Zaharopol). For Fréchet lattices (or more general locally convex solid Riesz spaces) there is virtually no information available. For a Fréchet lattice E , it is shown here that (amongst other things) every power-bounded linear operator on E is mean ergodic if and only if E is reflexive if and only if E is Dedekind σ-complete and every positive power-bounded operator on E is mean ergodic if and only if every positive power-bounded operator in the strong dual E ′ β (no longer a Fréchet lattice) is mean ergodic. An important technique is to develop criteria that detect when E admits a (positively) complemented lattice copy of c 0 , l 1 or l ∞ ." @default.
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• W2113127515 date "2011-09-26" @default.
• W2113127515 modified "2023-10-13" @default.
• W2113127515 title "Mean ergodic operators and reflexive Fréchet lattices" @default.
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• W2113127515 doi "https://doi.org/10.1017/s0308210510000314" @default.
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