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Cotype and absolutely summing homogeneous polynomials in ℒ p spaces

Daniel Pellegrino (2003)

Studia Mathematica

We lift to homogeneous polynomials and multilinear mappings a linear result due to Lindenstrauss and Pełczyński for absolutely summing operators. We explore the notion of cotype to obtain stronger results and provide various examples of situations in which the space of absolutely summing homogeneous polynomials is different from the whole space of homogeneous polynomials. Among other consequences, these results enable us to obtain answers to some open questions about absolutely summing homogeneous...

Duality, reflexivity and atomic decompositions in Banach spaces

Daniel Carando, Silvia Lassalle (2009)

Studia Mathematica

We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions....

Effective constructions of separable quotients of Banach spaces.

Marek Wójtowicz (1997)

Collectanea Mathematica

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.

Equivalences involving (p,q)-multi-norms

Oscar Blasco, H. G. Dales, Hung Le Pham (2014)

Studia Mathematica

We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form L r ( Ω ) , and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the [p,q]-concave multi-norm, and relate it to the standard t-multi-norm.

Equivanishing sequences of mappings

Piotr Antosik (2000)

Banach Center Publications

Utilizing elementary properties of convergence of numerical sequences we prove Nikodym, Banach, Orlicz-Pettis type theorems

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