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On the projectivity and flatness of some group modules

Gerhard Racher (2010)

Banach Center Publications

In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.

On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity.

María Jesús Carro (2002)

Publicacions Matemàtiques

Given a sublinear operator T satisfying that ||Tf||Lp(ν) ≤ C/(p-1) ||f||Lp(μ), for every 1 < p ≤ p0, with C independent of f and p, it was proved in [C] that... [check the paper abstract for the formula]This estimate implies that T: L log L → B, where B is a rearrangement invariant space. The purpose of this note is to give several characterizations of the space B and study its associate space. This last information allows us to formulate an extrapolation result of Zygmund type for linear...

On the relation between complex and real methods of interpolation

Mieczysław Mastyło, Vladimir Ovchinnikov (1997)

Studia Mathematica

We study those compatible couples of Banach spaces for which the complex method interpolation spaces are also described by the K-method of interpolation. As an application we present counter-examples to Cwikel's conjecture that all interpolation spaces of a Banach couple are described by the K-method whenever all complex interpolation spaces have this property.

On the structure of tensor norms related to (p,σ)-absolutely continuous operators.

Enrique A. Sánchez-Pérez (1996)

Collectanea Mathematica

We define an interpolation norm on tensor products of p-integrable function spaces and Banach spaces which satisfies intermediate properties between the Bochner norm and the injective norm. We obtain substitutes of the Chevet-Persson-Saphar inequalities for this case. We also use the calculus of traced tensor norms in order to obtain a tensor product description of the tensor norm associated to the interpolated ideal of (p, sigma)-absolutely continuous operators defined by Jarchow and Matter. As...

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