Displaying similar documents to “Interpolation of Banach lattices”

Interpolation of real method spaces via some ideals of operators

Mieczysław Mastyło, Mario Milman (1999)

Studia Mathematica

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Certain operator ideals are used to study interpolation of operators between spaces generated by the real method. Using orbital equivalence a new reiteration formula is proved for certain real interpolation spaces generated by ordered pairs of Banach lattices of the form ( X , L ∞ ( w ) ) . As an application we extend Ovchinnikov’s interpolation theorem from the context of classical Lions-Peetre spaces to a larger class of real interpolation spaces. A description of certain abstract J-method spaces is...

On equivalence of K- and J-methods for (n+1)-tuples of Banach spaces

Irina Asekritova, Natan Krugljak (1997)

Studia Mathematica

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It is shown that the main results of the theory of real interpolation, i.e. the equivalence and reiteration theorems, can be extended from couples to a class of (n+1)-tuples of Banach spaces, which includes (n+1)-tuples of Banach function lattices, Sobolev and Besov spaces. As an application of our results, it is shown that Lions' problem on interpolation of subspaces and Semenov's problem on interpolation of subcouples have positive solutions when all spaces are Banach function lattices...

The Lions's problem for Gustavsson-Peetre functor.

E.I. Bereznoi, Mieczyslaw Mastylo (1990)

Publicacions Matemàtiques

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The problem of coincidence of the interpolation spaces obtained by use of the interpolation method of Gustavsson-Peetre generated by (parameters) quasi-concave functions is investigated. It is shown that a restriction of this method to the class of all non-trivial Banach couples gives different interpolation spaces whenever two different parameters satisfying some conditions are used.

Effective constructions of separable quotients of Banach spaces.

Marek Wójtowicz (1997)

Collectanea Mathematica

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A simple way of obtaining separable quotients in the class of weakly countably determined (WCD) Banach spaces is presented. A large class of Banach lattices, possessing as a quotient c0, l1, l2, or a reflexive Banach space with an unconditional Schauder basis, is indicated.

On a result of Peetre about interpolation of operator spaces

Fernando Cobos, Teresa Signes (2000)

Publicacions Matemàtiques

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We establish interpolation formulæ for operator spaces that are components of a given quasi-normed operator ideal. Sometimes we assume that one of the couples involved is quasi-linearizable, some other times we assume injectivity or surjectivity in the ideal. We also show the necessity of these suppositions.