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On restricted weak upper semicontinuous set valued mappings and reflexivity

Julio Benítez, Vicente Montesinos (1999)

Bollettino dell'Unione Matematica Italiana

È noto che se uno spazio di Banach è quasi-smooth (cioè, la sua applicazione di dualità è debolmente semicontinua superiormente in senso ristretto), allora il suo duale non ha sottospazi chiusi normanti propri. Inoltre, se uno spazio di Banach ha una norma equivalente la cui applicazione di dualità ha un grafo che contiene superiormente un'applicazione debolmente semicontinua superiormente in senso ristretto, allora lo spazio è Asplund. Dimostriamo che se uno spazio di Banach ha una norma equivalente...

On S. Mazur's problems 8 and 88 from the Scottish Book

V. V. Peller (2007)

Studia Mathematica

The paper discusses Problems 8 and 88 posed by Stanisław Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Peller [J. Operator Theory 7 (1982)]. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper of Pełczyński and Sukochev in connection with Problem 88.

On scalar-valued nonlinear absolutely summing mappings

Daniel Pellegrino (2004)

Annales Polonici Mathematici

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.

On self-commutators of Toeplitz operators with rational symbols

Sherwin Kouchekian, James E. Thomson (2007)

Studia Mathematica

We prove that the self-commutator of a Toeplitz operator with unbounded analytic rational symbol has a dense domain in both the Bergman space and the Hardy space of the unit disc. This is a basic step towards establishing whether the self-commutator has a compact or trace-class extension.

On self-similar subgroups in the sense of IFS

Mustafa Saltan (2018)

Communications in Mathematics

In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterated function system (IFS). We then prove that some subgroups of p -adic numbers ℚ p are strong self-similar in the sense of IFS.

On set-valued cone absolutely summing maps

Coenraad Labuschagne, Valeria Marraffa (2010)

Open Mathematics

Spaces of cone absolutely summing maps are generalizations of Bochner spaces L p(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space ℒ 1 ∑ , c b f ( X ) of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L 1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of ℒ 1 ∑ , c b f ( X ) , and to derive necessary...

On Signorini problem for von Kármán equations. The case of angular domain

Jan Franců (1979)

Aplikace matematiky

The paper deals with the generalized Signorini problem. The used method of pseudomonotone semicoercive operator inequality is introduced in the paper by O. John. The existence result for smooth domains from the paper by O. John is extended to technically significant "angular" domains. The crucial point of the proof is the estimation of the nonlinear term which appears in the operator form of the problem. The substantial technical difficulties connected with non-smoothness of the boundary are overcome...

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