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The inclusion theorem for multiple summing operators

100%

Pérez-García D.

Studia Mathematica

2004

tom 165

nr 3

275-290

We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.

Algebrability of the set of non-convergent Fourier series

51%

Aron R., Pérez-García D., Seoane-Sepúlveda J.

Studia Mathematica

2006

tom 175

nr 1

83-90

We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.

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2 Studia Mathematica

2 Pérez-García D.

1 Aron R.

1 Seoane-Sepúlveda J.

1 2006

1 2004

Wyniki wyszukiwania

The inclusion theorem for multiple summing operators

Algebrability of the set of non-convergent Fourier series