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On scalar-valued nonlinear absolutely summing mappings

100%
Pellegrino D.
Annales Polonici Mathematici
|
2004
|
tom 83
|
nr 3
281-288
EN
We investigate cases ("coincidence situations") in which every scalar-valued continuous n-homogeneous polynomial (or every continuous n-linear mapping) is absolutely (p;q)-summing. We extend some well known coincidence situations and obtain several non-coincidence results, inspired by a linear technique due to Lindenstrauss and Pełczyński.
2
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Cotype and absolutely summing homogeneous polynomials in $ℒ_{p}$ spaces

100%
Pellegrino D.
Studia Mathematica
|
2003
|
tom 157
|
nr 2
121-131
EN
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 polynomials and multilinear mappings on $ℒ_{∞}$ spaces.
3
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Distinguished subspaces of $L_{p}$ of maximal dimension

45%
Botelho G., Cariello D., Fávaro V., Pellegrino D., Seoane-Sepúlveda J.
Studia Mathematica
|
2013
|
tom 215
|
nr 3
261-280
EN
Let (Ω,Σ,μ) be a measure space and 1 < p < ∞. We show that, under quite general conditions, the set $L_{p}(Ω) - ⋃_{1≤q
4
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When is the Haar measure a Pietsch measure for nonlinear mappings?

45%
Botelho G., Pellegrino D., Rueda P., Santos J., Seoane-Sepúlveda J.
Studia Mathematica
|
2012
|
tom 213
|
nr 3
275-287
EN
We show that, as in the linear case, the normalized Haar measure on a compact topological group G is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of C(G). This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed.
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