On operators from to or to
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.
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.
Jacek Dębecki (2016)
Czechoslovak Mathematical Journal
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We give a classification of all linear natural operators transforming -vectors (i.e., skew-symmetric tensor fields of type ) on -dimensional manifolds to tensor fields of type on , where is a Weil bundle, under the condition that , and . The main result of the paper states that, roughly speaking, each linear natural operator lifting -vectors to tensor fields of type on is a sum of operators obtained by permuting the indices of the tensor products of linear natural...
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.
Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)
Mathematica Bohemica
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Let be a complex Hilbert space, a positive operator with closed range in and the sub-algebra of of all -self-adjoint operators. Assume onto itself is a linear continuous map. This paper shows that if preserves -unitary operators such that then defined by is a homomorphism or an anti-homomorphism and for all , where and is the Moore-Penrose inverse of . A similar result is also true if preserves -quasi-unitary operators in both directions such that there...
Said Bouali, Youssef Bouhafsi (2015)
Mathematica Bohemica
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Let denote the algebra of operators on a complex infinite dimensional Hilbert space . For , the generalized derivation and the elementary operator are defined by and for all . In this paper, we exhibit pairs of operators such that the range-kernel orthogonality of holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of with respect to the wider class of unitarily invariant...
Anna Bednarska (2013)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We describe all -natural operators transforming projectable-projectable classical torsion-free linear connections on fibred-fibred manifolds into classical linear connections on cotangent bundles of . We show that this problem can be reduced to finding -natural operators for , and , .
Mohamed Amouch, Hamza Lakrimi (2024)
Mathematica Bohemica
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Let be a Banach space, the algebra of bounded linear operators on and an admissible Banach ideal of . For , let and denote the left and right multiplication defined by and , respectively. In this paper, we study the transmission of some concepts related to recurrent operators between , and their elementary operators and . In particular, we give necessary and sufficient conditions for and to be sequentially recurrent. Furthermore, we prove that is recurrent...
Ioana Ghenciu (2017)
Commentationes Mathematicae Universitatis Carolinae
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For Banach spaces and , let denote the space of all continuous compact operators from to endowed with the operator norm. A Banach space has the property if every Grothendieck subset of is relatively weakly compact. In this paper we study Banach spaces with property . We investigate whether the spaces and have the property, when and have the property.
G. L. Watson
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CONTENTSIntroduction.......................................................................................61. Definition of certain special forms...........................................62. Statement of results...................................................................83. Proof of Theorem 2.....................................................................94. Preliminaries for Theorem 1.....................................................105. Further preliminaries for Theorem...
B. A. Frasin (2012)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In this paper, we obtain new sufficient conditions for the operators and to be univalent in the open unit disc , where the functions belong to the classes and . The order of convexity for the operators and is also determined. Furthermore, and for , we obtain sufficient conditions for the operators and to be in the class . Several corollaries and consequences of the main results are also considered.
Hans Triebel (1994)
Studia Mathematica
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Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .
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 .
Sandro Manfredini, Simona Settepanella (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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Let be the -th ordered configuration space of all distinct points in the Grassmannian of -dimensional subspaces of , whose sum is a subspace of dimension . We prove that is (when non empty) a complex submanifold of of dimension and its fundamental group is trivial if , and and equal to the braid group of the sphere if . Eventually we compute the fundamental group in the special case of hyperplane arrangements, i.e. .
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 < ∞. ...
Jan Kurek, Włodzimierz M. Mikulski (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let be the category of -dimensional manifolds and local diffeomorphisms and let be the tangent functor on . Let be the category of real vector spaces and linear maps and let be the category of -dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors admitting -natural operators transforming classical linear connections on -dimensional manifolds into almost complex structures on .
Reynaldo Rojas-Hernández (2015)
Commentationes Mathematicae Universitatis Carolinae
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We show that any -product of at most -many -spaces has the -property. This result generalizes some known results about -spaces. On the other hand, we prove that every -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...
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.
Mats Andersson (2011)
Bulletin de la Société Mathématique de France
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Let be a coherent subsheaf of a locally free sheaf and suppose that has pure codimension. Starting with a residue current obtained from a locally free resolution of we construct a vector-valued Coleff-Herrera current with support on the variety associated to such that is in if and only if . Such a current can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed....
Joseph Kupka
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CONTENTS1. Introduction...................................................................................................... 52. Notation and basic terminology........................................................................... 73. Definition and basic properties of the spaces................................. 114. Integral representation of bounded linear functionals on ........ 235. Examples in theory...................................................................................
Shaban Khidr, Osama Abdelkader (2017)
Czechoslovak Mathematical Journal
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Let be a -convex intersection, , , in a complex manifold of complex dimension , , and let be a holomorphic vector bundle of rank over . In this paper, -estimates, , for solutions to the -equation with small loss of smoothness are obtained for -valued -forms on when . In addition, we solve the -equation with a support condition in -spaces. More precisely, we prove that for a -closed form in , , , with compact support and for with there...
E. Ferreyra, T. Godoy, M. Urciuolo (2002)
Colloquium Mathematicae
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Let , 1 ≤ i ≤ n, and for t > 0 and x = (x₁,...,xₙ) ∈ ℝⁿ, let , and . Let φ₁,...,φₙ be real functions in such that φ = (φ₁,..., φₙ) satisfies φ(t • x) = t ∘ φ(x). Let γ > 0 and let μ be the Borel measure on given by , where and dx denotes the Lebesgue measure on ℝⁿ. Let and let be the operator norm of from into , where the spaces are taken with respect to the Lebesgue measure. The type set is defined by . In the case for 1 ≤ i,k ≤ n we characterize the...