On a proof of the boundedness and nuclearity of pseudodifferential operators in
Jan A. Rempała (1990)
Annales Polonici Mathematici
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Jan A. Rempała (1990)
Annales Polonici Mathematici
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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.
Ioana Ghenciu (2023)
Commentationes Mathematicae Universitatis Carolinae
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We introduce the definition of -limited completely continuous operators, . The question of whether a space of operators has the property that every -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using -limited completely continuous evaluation operators.
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...
Kevin Esmeral, Osmin Ferrer, Jorge Jalk, Boris Lora Castro (2019)
Archivum Mathematicum
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In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators for which there exists a fundamental decomposition of the Krein space with and invariant under .
B. Mirković (1970)
Matematički Vesnik
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Teresa Winiarska, Tadeusz Winiarski (2003)
Annales Polonici Mathematici
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The purpose of this paper is to provide a method of reduction of some problems concerning families of linear operators with domains to a problem in which all the operators have the same domain . To do it we propose to construct a family of automorphisms of a given Banach space X having two properties: (i) the mapping is sufficiently regular and (ii) for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition...
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.
T. Maćkowiak (1976)
Colloquium Mathematicae
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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].
Bojan Magajna (1993)
Studia Mathematica
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Given two n-tuples and of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in .
(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.
Anthony Hester, Claudio H. Morales (2020)
Commentationes Mathematicae Universitatis Carolinae
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Consider the Mann iteration for a nonexpansive mapping defined on some subset of the normed space . We present an innovative proof of the Ishikawa almost fixed point principle for nonexpansive mapping that reveals deeper aspects of the behavior of the process. This fact allows us, among other results, to derive convergence of the process under the assumption of existence of an accumulation point of .
Edvard Kramar (2016)
Commentationes Mathematicae Universitatis Carolinae
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Denote by the commutator of two bounded operators and acting on a locally convex topological vector space. If , we show that is a quasinilpotent operator and we prove that if is a compact operator, then is a Riesz operator.
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 < ∞.
Deba P. Sinha, Anil K. Karn (2002)
Studia Mathematica
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For p ≥ 1, a subset K of a Banach space X is said to be relatively p-compact if , where p’ = p/(p-1) and . An operator T ∈ B(X,Y) is said to be p-compact if T(Ball(X)) is relatively p-compact in Y. Similarly, weak p-compactness may be defined by considering . It is proved that T is (weakly) p-compact if and only if T* factors through a subspace of in a particular manner. The normed operator ideals of p-compact operators and of weakly p-compact operators, arising from these factorizations,...
Manuel González, Eero Saksman, Hans-Olav Tylli (1995)
Studia Mathematica
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For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E**/E) is defined by R(S)(x** + E) = S**x** + E(x** ∈ E**). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W(E) (here W(E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non-zero compact operators in Im(R) in the case of and C(0,1), but R(L(E)/W(E)) identifies isometrically...
Claudia Garetto (2010)
Banach Center Publications
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We provide a deep investigation of the notions of - and -hypoellipticity for partial differential operators with constant Colombeau coefficients. This involves generalized polynomials and fundamental solutions in the dual of a Colombeau algebra. Sufficient conditions and necessary conditions for - and -hypoellipticity are given
Nizar Jaoua (1999)
Studia Mathematica
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We study the order boundedness of composition operators induced by holomorphic self-maps of the open unit disc D. We consider these operators first on the Hardy spaces 0 < p < ∞ and then on the Nevanlinna class N. Given a non-negative increasing function h on [0,∞[, a composition operator is said to be X,Lh-order bounded (we write (X,Lh)-ob) with or X = N if its composition with the map f ↦ f*, where f* denotes the radial limit of f, is order bounded from X into . We give...
A. Takači (1978)
Matematički Vesnik
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Daniel Galicer, Silvia Lassalle, Pablo Turco (2012)
Studia Mathematica
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We study the space of p-compact operators, , using the theory of tensor norms and operator ideals. We prove that is associated to , the left injective associate of the Chevet-Saphar tensor norm (which is equal to ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that is equal to for a wide range of values of p and q, and show that our results...
Rodrigo Hidalgo Linares, Oleg Okunev (2023)
Commentationes Mathematicae Universitatis Carolinae
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We study the relation of -equivalence defined between Tychonoff spaces, that is, we study the topological isomorphisms of their respective free locally convex spaces. We introduce the concept of an -retract in a Tychonoff space in terms of the existence of a special kind of simultaneous extensions of continuous functions, explore the relation of this concept with the Dugundji extension theorem, and find some conditions that allow us to identify -retracts in various classes of topological...