Inequalities between absolutely (p,q)-summing norms

B. Carl

Displaying similar documents to “Inequalities between absolutely (p,q)-summing norms”

A generalization of Khintchine's inequality and its application in the theory of operator ideals

E. Gluskin, A. Pietsch, J. Puhl (1980)

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Banach ideals on Hilbert spaces

Y. Gordon, D. Lewis (1975)

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Characterization of (p,q,r)-absolutely summing operators on Hilbert space

Deborah Allinger (1981)

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Absolutely summing operators between Banach spaces of finite cotype.

E. A. Sánchez Pérez (2000)

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Small ideals of operators

Albrecht Pietsch (1974)

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Best constants and asymptotics of Marcinkiewicz-Zygmund inequalities

Andreas Defant, Marius Junge (1997)

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We determine the set of all triples 1 ≤ p,q,r ≤ ∞ for which the so-called Marcinkiewicz-Zygmund inequality is satisfied: There exists a constant c≥ 0 such that for each bounded linear operator $T : L_{q} (μ) \to L_{p} (ν)$ , each n ∈ ℕ and functions $f_{1}, . . ., f_{n} \in L_{q} (μ)$ , $(ʃ (\sum_{k = 1}^{n} | T f_{k} |^{r})^{p / r} {d ν)}^{1 / p} \leq c ∥ T ∥ (ʃ (\sum_{k = 1}^{n} | f_{k} |^{r} {)^{q / r} d μ)}^{1 / q}$ . This type of inequality includes as special cases well-known inequalities of Paley, Marcinkiewicz, Zygmund, Grothendieck, and Kwapień. If such a Marcinkiewicz-Zygmund inequality holds for a given triple (p,q,r), then we calculate the best constant c ≥ 0 (with the...

On some matrix Inequalities in Banach Spaces

Andreas Defant, Marius Junge (1996)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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On the surjective (injective) envelope of strictly (co-) singular operators

Lutz Weis (1976)

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On a theorem of L. Schwartz and its applications to absolutely summing operators

S. Kwapień (1970)

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The Grothendieck-Pietsch domination principle for nonlinear summing integral operators

Karl Lermer (1998)

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We transform the concept of p-summing operators, 1≤ p < ∞, to the more general setting of nonlinear Banach space operators. For 1-summing operators on B(Σ,X)-spaces having weak integral representations we generalize the Grothendieck-Pietsch domination principle. This is applied for the characterization of 1-summing Hammerstein operators on C(S,X)-spaces. For p-summing Hammerstein operators we derive the existence of control measures and p-summing extensions to B(Σ,X)-spaces. ...