On the Dunford-Pettis property of tensor product spaces

Ioana Ghenciu

Displaying similar documents to “On the Dunford-Pettis property of tensor product spaces”

The reciprocal Dunford–Pettis property of order $p$ in projective tensor products

Ioana Ghenciu (2019)

Commentationes Mathematicae Universitatis Carolinae

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We investigate whether the projective tensor product of two Banach spaces $X$ and $Y$ has the reciprocal Dunford–Pettis property of order $p$ , $1 \leq p < \infty$ , when $X$ and $Y$ have the respective property.

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...

Some isomorphic properties in projective tensor products

Ioana Ghenciu (2022)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient conditions implying that the projective tensor product of two Banach spaces $X$ and $Y$ has the $p$ -sequentially Right and the $p$ - $L$ -limited properties, $1 \leq p < \infty$ .

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...

The classical subspaces of the projective tensor products of $ℓ_{p}$ and C(α) spaces, α < ω₁

Elói Medina Galego, Christian Samuel (2013)

Studia Mathematica

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We completely determine the $ℓ_{q}$ and C(K) spaces which are isomorphic to a subspace of $ℓ_{p} \otimes ̂_{π} C (α)$ , the projective tensor product of the classical $ℓ_{p}$ space, 1 ≤ p < ∞, and the space C(α) of all scalar valued continuous functions defined on the interval of ordinal numbers [1,α], α < ω₁. In order to do this, we extend a result of A. Tong concerning diagonal block matrices representing operators from $ℓ_{p}$ to ℓ₁, 1 ≤ p < ∞. The first main theorem is an extension of a result of E. Oja and states...

Property $(𝐰𝐋)$ and the reciprocal Dunford-Pettis property in projective tensor products

Ioana Ghenciu (2015)

Commentationes Mathematicae Universitatis Carolinae

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A Banach space $X$ has the reciprocal Dunford-Pettis property ( $R D P P$ ) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $R D P P$ (resp. property $(w L)$ ) if every $L$ -subset of $X^{*}$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes_{π} Y$ has property $(w L)$ when $X$ has the $R D P P$ , $Y$ has property $(w L)$ , and $L (X, Y^{*}) = K (X, Y^{*})$ .

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.

Tensor products of higher almost split sequences in subcategories

Xiaojian Lu, Deren Luo (2023)

Czechoslovak Mathematical Journal

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We introduce the algebras satisfying the $(ℬ, n)$ condition. If $Λ$ , $Γ$ are algebras satisfying the $(ℬ, n)$ , $(ℰ, m)$ condition, respectively, we give a construction of $(m + n)$ -almost split sequences in some subcategories ${(ℬ \otimes ℰ)}^{(i_{0}, j_{0})}$ of $mod (Λ \otimes Γ)$ by tensor products and mapping cones. Moreover, we prove that the tensor product algebra $Λ \otimes Γ$ satisfies the $({(ℬ \otimes ℰ)}^{(i_{0}, j_{0})}, n + m)$ condition for some integers $i_{0}$ , $j_{0}$ ; this construction unifies and extends the work of A. Pasquali (2017), (2019).

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.

Application of $(L)$ sets to some classes of operators

Kamal El Fahri, Nabil Machrafi, Jawad H&#039;michane, Aziz Elbour (2016)

Mathematica Bohemica

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The paper contains some applications of the notion of $Ł$ sets to several classes of operators on Banach lattices. In particular, we introduce and study the class of order $(L)$ -Dunford-Pettis operators, that is, operators from a Banach space into a Banach lattice whose adjoint maps order bounded subsets to an $(L)$ sets. As a sequence characterization of such operators, we see that an operator $T : X \to E$ from a Banach space into a Banach lattice is order $Ł$ -Dunford-Pettis, if and only if $| T (x_{n}) | \to 0$ for $σ (E, E^{'})$ for every...

A Study on $φ$ -recurrence $τ$ -curvature tensor in $(k, μ)$ -contact metric manifolds

Gurupadavva Ingalahalli, C.S. Bagewadi (2018)

Communications in Mathematics

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In this paper we study $φ$ -recurrence $τ$ -curvature tensor in $(k, μ)$ -contact metric manifolds.

Finite groups of OTP projective representation type

Leonid F. Barannyk (2012)

Colloquium Mathematicae

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Let K be a field of characteristic p > 0, K* the multiplicative group of K and $G = G_{p} \times B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $K^{λ} G$ a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable $K^{λ} G$ -module is isomorphic to the outer tensor product V W of an indecomposable $K^{λ} G_{p}$ -module...

Linear natural operators lifting $p$ -vectors to tensors of type $(q, 0)$ on Weil bundles

Jacek Dębecki (2016)

Czechoslovak Mathematical Journal

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We give a classification of all linear natural operators transforming $p$ -vectors (i.e., skew-symmetric tensor fields of type $(p, 0)$ ) on $n$ -dimensional manifolds $M$ to tensor fields of type $(q, 0)$ on $T^{A} M$ , where $T^{A}$ is a Weil bundle, under the condition that $p \geq 1$ , $n \geq p$ and $n \geq q$ . The main result of the paper states that, roughly speaking, each linear natural operator lifting $p$ -vectors to tensor fields of type $(q, 0)$ on $T^{A}$ is a sum of operators obtained by permuting the indices of the tensor products of linear natural...

(E,F)-Schur multipliers and applications

Fedor Sukochev, Anna Tomskova (2013)

Studia Mathematica

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For two given symmetric sequence spaces E and F we study the (E,F)-multiplier space, that is, the space of all matrices M for which the Schur product M ∗ A maps E into F boundedly whenever A does. We obtain several results asserting continuous embedding of the (E,F)-multiplier space into the classical (p,q)-multiplier space (that is, when $E = l_{p}$ , $F = l_{q}$ ). Furthermore, we present many examples of symmetric sequence spaces E and F whose projective and injective tensor products are not isomorphic...

Limited $p$ -converging operators and relation with some geometric properties of Banach spaces

Mohammad B. Dehghani, Seyed M. Moshtaghioun (2021)

Commentationes Mathematicae Universitatis Carolinae

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By using the concepts of limited $p$ -converging operators between two Banach spaces $X$ and $Y$ , $L_{p}$ -sets and $L_{p}$ -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as $*$ -Dunford–Pettis property of order $p$ and Pelczyński’s property of order $p$ , $1 \leq p < \infty$ .

Tensor product of left n-invertible operators

B. P. Duggal, Vladimir Müller (2013)

Studia Mathematica

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A Banach space operator T ∈ has a left m-inverse (resp., an essential left m-inverse) for some integer m ≥ 1 if there exists an operator S ∈ (resp., an operator S ∈ and a compact operator K ∈ ) such that $\sum_{i = 0}^{m} {(- 1)}^{i} (\binom{m}{i}) S^{m - i} T^{m - i} = 0$ (resp., $\sum_{i = 0}^{m} {(- 1)}^{i} (\binom{m}{i}) T^{m - i} S^{m - i} = K$ ). If $T_{i}$ is left $m_{i}$ -invertible (resp., essentially left $m_{i}$ -invertible), then the tensor product T₁ ⊗ T₂ is left (m₁ + m₂-1)-invertible (resp., essentially left (m₁ + m₂-1)-invertible). Furthermore, if T₁ is strictly left m-invertible (resp., strictly essentially left m-invertible),...

Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic

Leonid F. Barannyk, Dariusz Klein (2012)

Colloquium Mathematicae

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Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and $G = G_{p} \times B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $S^{λ} G$ the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable...