Coincidence of topologies on tensor products of Köthe echelon spaces

J. Bonet; A. Defant; A. Peris; M. Ramanujan

Displaying similar documents to “Coincidence of topologies on tensor products of Köthe echelon spaces”

Biduals of tensor products in operator spaces

Verónica Dimant, Maite Fernández-Unzueta (2015)

Studia Mathematica

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We study whether the operator space $V * * \overset{α}{\otimes} W * *$ can be identified with a subspace of the bidual space $(V \overset{α}{\otimes} W) * *$ , for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be...

On the derived tensor product functors for (DF)- and Fréchet spaces

Oğuz Varol (2007)

Studia Mathematica

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For a (DF)-space E and a tensor norm α we investigate the derivatives $T o r_{α}^{l} (E, \cdot)$ of the tensor product functor $E \otimes ̃_{α} \cdot : \to$ from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of $T o r ¹_{α} (E, F)$ , which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.

On the Dunford-Pettis property of tensor product spaces

Ioana Ghenciu (2011)

Colloquium Mathematicae

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We give sufficient conditions on Banach spaces E and F so that their projective tensor product $E \otimes_{π} F$ and the duals of their projective and injective tensor products do not have the Dunford-Pettis property. We prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T:E* → F** is completely continuous, then $(E \otimes_{ϵ} F) *$ does not have the DPP. We also prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T: F** → E* is...

The associated tensor norm to $(q, p)$ -absolutely summing operators on $C (K)$ -spaces

J. A. López Molina, Enrique A. Sánchez-Pérez (1997)

Czechoslovak Mathematical Journal

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We give an explicit description of a tensor norm equivalent on $C (K) \otimes F$ to the associated tensor norm $ν_{q p}$ to the ideal of $(q, p)$ -absolutely summing operators. As a consequence, we describe a tensor norm on the class of Banach spaces which is equivalent to the left projective tensor norm associated to $ν_{q p}$ .

Diagonals of projective tensor products and orthogonally additive polynomials

Qingying Bu, Gerard Buskes (2014)

Studia Mathematica

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Let E be a Banach space with 1-unconditional basis. Denote by $Δ (\otimes ̂_{n, π} E)$ (resp. $Δ (\otimes ̂_{n, s, π} E)$ ) the main diagonal space of the n-fold full (resp. symmetric) projective Banach space tensor product, and denote by $Δ (\otimes ̂_{n, | π |} E)$ (resp. $Δ (\otimes ̂_{n, s, | π |} E)$ ) the main diagonal space of the n-fold full (resp. symmetric) projective Banach lattice tensor product. We show that these four main diagonal spaces are pairwise isometrically isomorphic, and in addition, that they are isometrically lattice isomorphic to $E_{[n]}$ , the completion of the n-concavification...

How many are equiaffine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2015)

Archivum Mathematicum

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The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.

A new way to iterate Brzeziński crossed products

Leonard Dăuş, Florin Panaite (2016)

Colloquium Mathematicae

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If $A \otimes_{R, σ} V$ and $A \otimes_{P, ν} W$ are two Brzeziński crossed products and Q: W⊗ V → V⊗ W is a linear map satisfying certain properties, we construct a Brzeziński crossed product $A \otimes_{S, θ} (V \otimes W)$ . This construction contains as a particular case the iterated twisted tensor product of algebras.

On torsion of a $3$ -web

Alena Vanžurová (1995)

Mathematica Bohemica

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A 3-web on a smooth $2 n$ -dimensional manifold can be regarded locally as a triple of integrable $n$ -distributions which are pairwise complementary, [5]; that is, we can work on the tangent bundle only. This approach enables us to describe a $3$ -web and its properties by invariant $(1, 1)$ -tensor fields $P$ and $B$ where $P$ is a projector and $B^{2} =$ id. The canonical Chern connection of a web-manifold can be introduced using this tensor fields, [1]. Our aim is to express the torsion tensor $T$ of the Chern connection...

Equivalences involving (p,q)-multi-norms

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 $L^{r} (Ω)$ , 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.

Centers of n-fold tensor products of graphs

Sarah Bendall, Richard Hammack (2004)

Discussiones Mathematicae Graph Theory

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Formulas for vertex eccentricity and radius for the n-fold tensor product $G = \otimes_{i = 1} ⁿ G_{i}$ of n arbitrary simple graphs $G_{i}$ are derived. The center of G is characterized as the union of n+1 vertex sets of form V₁×V₂×...×Vₙ, with $V_{i} \subseteq V (G_{i})$ .

On completely bounded bimodule maps over W*-algebras

Bojan Magajna (2003)

Studia Mathematica

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It is proved that for a von Neumann algebra A ⊆ B(ℋ ) the subspace of normal maps is dense in the space of all completely bounded A-bimodule homomorphisms of B(ℋ ) in the point norm topology if and only if the same holds for the corresponding unit balls, which is the case if and only if A is atomic with no central summands of type $I_{\infty, \infty}$ . Then a duality result for normal operator modules is presented and applied to the following problem. Given an operator space X and a von Neumann algebra...

On isomorphic classification of tensor products $E_{\infty} (a) \otimes ̂ E_{\infty}^{'} (b)$

Goncharov A., Zahariuta V., Terzioğlu Tosun

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Abstract New linear topological invariants are introduced and utilized to give an isomorphic classification of tensor products of the type $E_{\infty} (a) \otimes ̂ E_{\infty}^{'} (b)$ , where $E_{\infty} (a)$ is a power series space of infinite type. These invariants are modifications of those suggested earlier by Zahariuta. In particular, some new results are obtained for spaces of infinitely differentiable functions with values in a locally convex space X. These spaces coincide, up to isomorphism, with spaces L(s’,X) of all continuous linear...

The tensor algebra of power series spaces

Dietmar Vogt (2009)

Studia Mathematica

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The linear isomorphism type of the tensor algebra T(E) of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always s, the situation for finite type power series spaces is more complicated. The linear isomorphism T(s) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra $s_{•}$ . This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet...

Locally pointwise superconvergence of the tensor-product finite element in three dimensions

Jinghong Liu, Liu, Wen, Qiding Zhu (2019)

Applications of Mathematics

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Consider a second-order elliptic boundary value problem in three dimensions with locally smooth coefficients and solution. Discuss local superconvergence estimates for the tensor-product finite element approximation on a regular family of rectangular meshes. It will be shown that, by the estimates for the discrete Green’s function and discrete derivative Green’s function, and the relationship of norms in the finite element space such as $L^{2}$ -norms, $W^{1, \infty}$ -norms, and negative-norms in locally...