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The cofinal property of the reflexive indecomposable Banach spaces

Spiros A. Argyros, Theocharis Raikoftsalis (2012)

Annales de l’institut Fourier

It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably p -saturated space with 1 < p < and of a c 0 saturated space.

The commutators of analysis and interpolation

Cerdà, Joan (2003)

Nonlinear Analysis, Function Spaces and Applications

The boundedness properties of commutators for operators are of central importance in Mathematical Analysis, and some of these commutators arise in a natural way from interpolation theory. Our aim is to present a general abstract method to prove the boundedness of the commutator [ T , Ω ] for linear operators T and certain unbounded operators Ω that appear in interpolation theory, previously known and a priori unrelated for both real and complex interpolation methods, and also to show how the abstract result...

The Lizorkin-Freitag formula for several weighted L p spaces and vector-valued interpolation

Irina Asekritova, Natan Krugljak, Ludmila Nikolova (2005)

Studia Mathematica

A complete description of the real interpolation space L = ( L p ( ω ) , . . . , L p ( ω ) ) θ , q is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces Ω i (i ∈ I) such that L is an l q sum of the restrictions of L to Ω i , and L on each Ω i is a result of interpolation of just two weighted L p spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.

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