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Some permanence results of properties of Banach spaces

Giovanni Emmanuele (2004)

Commentationes Mathematicae Universitatis Carolinae

Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.

Some problems for measures on non-standard algebraic structures

Maria Gabriella Graziano (2000)

Bollettino dell'Unione Matematica Italiana

Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli aspetti topologici...

Some problems on narrow operators on function spaces

Mikhail Popov, Evgenii Semenov, Diana Vatsek (2014)

Open Mathematics

It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i....

Some properties and applications of equicompact sets of operators

E. Serrano, C. Piñeiro, J. M. Delgado (2007)

Studia Mathematica

Let X and Y be Banach spaces. A subset M of (X,Y) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xₙ) in X has a subsequence ( x k ( n ) ) such that ( T x k ( n ) ) is uniformly convergent for T ∈ M. We study the relationship between this concept and the notion of uniformly completely continuous set and give some applications. Among other results, we obtain a generalization of the classical Ascoli theorem and a compactness criterion...

Currently displaying 501 – 520 of 1282