On d-characteristic and -characteristic of linear operators
D. Przeworska-Rolewicz, S. Rolewicz (1967)
Annales Polonici Mathematici
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D. Przeworska-Rolewicz, S. Rolewicz (1967)
Annales Polonici Mathematici
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A. Takači (1978)
Matematički Vesnik
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Z. Kominek (1974)
Annales Polonici Mathematici
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C. T. Ng (1973)
Annales Polonici Mathematici
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H. Światak (1967)
Annales Polonici Mathematici
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M. Malenica (1982)
Matematički Vesnik
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Yasutaka Sibuya (1984)
Recherche Coopérative sur Programme n°25
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Ioana Ghenciu, Paul Lewis (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space , as well as the complementation of the space of w*-w compact operators in the space of w*-w operators from X* to Y.
Feng Qin (2015)
Kybernetika
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Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. In the case of bisymmetric aggregation operators with the neutral elements, Saminger, Mesiar and Dubois, already reduced characterization of commuting -ary operators to resolving the unary distributive functional equations. And then the full characterizations of these equations are obtained under the assumption that...
Sunanda Naik (2010)
Annales Polonici Mathematici
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Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators is bounded on the Dirichlet spaces . We also give a short and direct proof of boundedness of on the Hardy space for 1 < p < ∞.
Min Zhang, Jianguo Si (2014)
Annales Polonici Mathematici
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This work deals with Feigenbaum’s functional equation ⎧ , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.
Z. Krzeszowiak (1969)
Annales Polonici Mathematici
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Elói Medina Galego (2011)
Colloquium Mathematicae
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We classify, up to isomorphism, the spaces of compact operators (E,F), where E and F are the Banach spaces of all continuous functions defined on the compact spaces , the topological products of Cantor cubes and intervals of ordinal numbers [0,α].
Christian Le Merdy (2004)
Bulletin de la Société Mathématique de France
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We give new results on square functions associated to a sectorial operator on for . Under the assumption that is actually -sectorial, we prove equivalences of the form for suitable functions . We also show that has a bounded functional calculus with respect to . Then we apply our results to the study of conditions under which we have an estimate , when generates a bounded semigroup on and is a linear mapping.
Teresa Janiak, Elżbieta Łuczak-Kumorek (1996)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧ (0) ⎨ ⎩ (1)
W. M. Mikulski (2002)
Colloquium Mathematicae
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Let r and n be natural numbers. For n ≥ 2 all natural operators transforming vector fields on n-manifolds M to 1-forms on are classified. For n ≥ 3 all natural operators transforming vector fields on n-manifolds M to 2-forms on are completely described.
Earl Berkson, T. A. Gillespie (2005)
Studia Mathematica
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For 1 ≤ q < ∞, let denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction...
Dumitru Popa (2013)
Studia Mathematica
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Let 1 ≤ p < ∞, be a sequence of Banach spaces and the coresponding vector valued sequence space. Let , be two sequences of Banach spaces, , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator by . We give necessary and sufficient conditions for to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞. ...
Andreas M. Fröhlich, Lutz Weis (2006)
Bulletin de la Société Mathématique de France
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We characterise the boundedness of the calculus of a sectorial operator in terms of dilation theorems. We show e. g. that if generates a bounded analytic semigroup on a UMD space, then the calculus of is bounded if and only if has a dilation to a bounded group on . This generalises a Hilbert space result of C.LeMerdy. If is an space we can choose another space in place of .
J. Kurek, W. M. Mikulski (2003)
Colloquium Mathematicae
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For natural numbers n ≥ 3 and r a complete description of all natural bilinear operators is presented. Next for natural numbers r and n ≥ 3 a full classification of all natural linear operators is obtained.
William Johnson, Gideon Schechtman (2008)
Journal of the European Mathematical Society
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A classification of weakly compact multiplication operators on 1<p<ppLpTLp1<p<2pT|XXLpXLrr<2XIt is also shown that if is convolution by a biased coin on of the Cantor group, , and is an isomorphism for some reflexive subspace of , then is isomorphic to a Hilbert space. The case answers a question asked by Rosenthal in 1976.
Janusz Morawiec, Ludwig Reich (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let 0 < β < α < 1 and let p ∈ (0,1). We consider the functional equation φ(x) = pφ (x-β)/(1-β) + (1-p)φ(minx/α, (x(α-β)+β(1-α))/α(1-β)) and its solutions in two classes of functions, namely ℐ = φ: ℝ → ℝ|φ is increasing, , , = φ: ℝ → ℝ|φ is continuous, , . We prove that the above equation has at most one solution in and that for some parameters α,β and p such a solution exists, and for some it does not. We also determine all solutions of the equation in ℐ and we show the...
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Krzysztof Zajkowski (2005)
Banach Center Publications
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We consider operators acting in the space C(X) (X is a compact topological space) of the form , u ∈ C(X), where and are given continuous mappings (1 ≤ k ≤ N). A new formula on the logarithm of the spectral radius r(A) is obtained. The logarithm of r(A) is defined as a nonlinear functional λ depending on the vector of functions . We prove that , where Mes is the set of all probability vectors of measures on X × 1,..., N and λ* is some convex lower-semicontinuous functional on...