A remark on p-absolutely summing operators in -spaces
S. Kwapień (1970)
Studia Mathematica
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S. Kwapień (1970)
Studia Mathematica
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Nicole Tomczak (1970)
Studia Mathematica
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A. Pietsch (1970-1971)
Séminaire Équations aux dérivées partielles (Polytechnique)
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(2011)
Banach Center Publications
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Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let and be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.
B. Carl (1976)
Studia Mathematica
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Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2009)
Studia Mathematica
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Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides...
Kamil John (2000)
Commentationes Mathematicae Universitatis Carolinae
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Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let and be Banach spaces such that is weakly compactly generated Asplund space and has the approximation property (respectively is weakly compactly generated Asplund space and has the approximation property). Suppose that and let . Then (respectively ) can be equivalently renormed so that any projection of onto has the sup-norm greater or equal to . ...
M. A. Fugarolas (2004)
Colloquium Mathematicae
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Let Π₂ be the operator ideal of all absolutely 2-summing operators and let be the identity map of the m-dimensional linear space. We first establish upper estimates for some mixing norms of . Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to Π₂; in this context, we also...
Dumitru Popa (2014)
Studia Mathematica
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We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of spaces. This characterization is used to show that multiple s-summing operators on a product of spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators such that none of the associated linear operators...
Oscar Blasco, H. G. Dales, Hung Le Pham (2014)
Studia Mathematica
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We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form , 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.
Kirsti Mattila (2011)
Studia Mathematica
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We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the...
Jean-Matthieu Augé (2012)
Studia Mathematica
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Let T be a bounded linear operator on a (real or complex) Banach space X. If (aₙ) is a sequence of non-negative numbers tending to 0, then the set of x ∈ X such that ||Tⁿx|| ≥ aₙ||Tⁿ|| for infinitely many n’s has a complement which is both σ-porous and Haar-null. We also compute (for some classical Banach space) optimal exponents q > 0 such that for every non-nilpotent operator T, there exists x ∈ X such that , using techniques which involve the modulus of asymptotic uniform smoothness...
Jolanta Socała (1998)
Annales Polonici Mathematici
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Asymptotic convergence theorems for nonnegative operators on Banach lattices, on , on C(X) and on are proved. The general results are applied to a class of integral operators on L¹.
P. Lewis (2001)
Studia Mathematica
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Bessaga and Pełczyński showed that if c₀ embeds in the dual X* of a Banach space X, then ℓ¹ embeds complementably in X, and embeds as a subspace of X*. In this note the Diestel-Faires theorem and techniques of Kalton are used to show that if X is an infinite-dimensional Banach space, Y is an arbitrary Banach space, and c₀ embeds in L(X,Y), then embeds in L(X,Y), and ℓ¹ embeds complementably in . Applications to embeddings of c₀ in various spaces of operators are given.
Jan Stochel, F. H. Szafraniec (1997)
Annales Polonici Mathematici
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The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.