On the Space lp+ = ∩lqq&gt;p

Metafune, Giorgio; Moscatelli, V. B.

doi:10.1002/mana.19901470102

Cited by 27 publications

(20 citation statements)

References 3 publications

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“…[22]). We also mention`p + , 1 p < 1 (see [23]) and L p , 1 < p < 1 (see [11]). Further examples are L ) consisting of the p-th power m-integrable (respectively, weakly m-integrable) functions are Fréchet lattices (see [9], [10], [25]).…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Mean ergodic operators and reflexive Fréchet lattices

Bonet¹,

Pagter²,

Ricker³

2011

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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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, Wol¤ and Zaharopol cited in the references. 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 (amongst other things) that every power bounded linear operator on E is mean ergodic if and only if E is re ‡exive if and only if E is Dedekind -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 0 (no longer a Fréchet lattice) is mean ergodic. An important technique is to develop criteria which detect when E admits a (positively) complemented lattice copy of c0,`1 or`1.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Mean ergodic operators and reflexive Fréchet lattices

Bonet¹,

Pagter²,

Ricker³

2011

Proceedings of the Royal Society of Edinburgh: Section A Mathem

View full text Add to dashboard Cite

show abstract

“…We will use the Fréchet spaces l q + = p>q l p and L q − = p<q L p ([0, 1]) (these spaces have an interest in the structure theory of Fréchet spaces and are primary and have all nuclear Λ 1 (α)-spaces as complemented subspaces, see [27,3] …”

Section: An Embedding Theoremmentioning

confidence: 99%