scholarly journals Some stability properties of c0-saturated spaces

1995 ◽  
Vol 118 (2) ◽  
pp. 287-301 ◽  
Author(s):  
Denny H. Leung
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Tensor Products ◽  
General Version ◽  
Direct Sums ◽  
Stability Properties ◽  
Infinite Dimensional ◽  
The Stability

AbstractA Banach space is c0-saturated if all of its closed infinite-dimensional subspaces contain an isomorph of c0. In this article, we study the stability of this property under the formation of direct sums and tensor products. Some of the results are: (1) a slightly more general version of the fact that c0-sums of c0-saturated spaces are c0-saturated; (2) C(K, E) is c0-saturated if both C(K) and E are; (3) the tensor product is c0-saturated, where JH is the James Hagler space

scholarly journals The dual of the space of bounded operators on a Banach space

2021 ◽  
Vol 8 (1) ◽  
pp. 48-59
Author(s):  
Fernanda Botelho ◽  
Richard J. Fleming
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Dual Space ◽  
Tensor Products ◽  
Bounded Operators ◽  
Projective Tensor Product ◽  
Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

scholarly journals Positive p-summing operators, vector measures and tensor products

1988 ◽  
Vol 31 (2) ◽  
pp. 179-184 ◽  
Author(s):  
Oscar Blasco
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Lattice ◽  
Tensor Products ◽  
Boundary Values ◽  
Vector Measures ◽  
Absolutely Summing Operators

In this paper we shall introduce a certain class of operators from a Banach lattice X into a Banach space B (see Definition 1) which is closely related to p-absolutely summing operators defined by Pietsch [8].These operators, called positive p-summing, have already been considered in [9] in the case p = 1 (there they are called cone absolutely summing, c.a.s.) and in [1] by the author who found this space to be the space of boundary values of harmonic B-valued functions in .Here we shall use these spaces and the space of majorizing operators to characterize the space of bounded p-variation measures and to endow the tensor product with a norm in order to get as its completion in this norm.

Tensor products which do not preserve operator algebras

1990 ◽  
Vol 108 (2) ◽  
pp. 395-403 ◽  
Author(s):  
David P. Blecher
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Operator Algebras ◽  
Tensor Products ◽  
Preserve Operator ◽  
Infinite Dimensional ◽  
Hilbert Space Operators ◽  
Algebra Of Operators

Of late the link between operator algebras and certain tensor products has been reiterated [5]. We prove here that the projective and Haagerup tensor products of two infinite-dimensional C*-algebras is not even topologically isomorphic to an algebra of operators on a Hilbert space. Estimates are given for the distance of the tensor product from such an algebra. Nonetheless with respect to a natural multiplication the Haagerup tensor product of two algebras of Hilbert space operators is completely isometrically isomorphic to an algebra of operators on some B(ℋ).

scholarly journals On Banach spaces with Mazur's property

1991 ◽  
Vol 33 (1) ◽  
pp. 51-54 ◽  
Author(s):  
Denny H. Leung
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Tensor Products ◽  
Continuous Functional ◽  
The Stability

A Banach space E is said to have Mazur's property if every weak* sequentially continuous functional in E” is weak* continuous, i.e. belongs to E. Such spaces were investigated in [5] and [9] where they were called d-complete and μB-spaces respectively. The class of Banach spaces with Mazur's property includes the WCG spaces and, more generally, the Banach spaces with weak* angelic dual balls [4, p. 564]. Also, it is easy to see that Mazur's property is inherited by closed subspaces. The main goal of this paper is to present generalizations of some results of [5] concerning the stability of Mazur's property with respect to forming some tensor products of Banach spaces. In particular, we show in Sections 2 and 3 that the spaces E ⊗εF and Lp(μ, E) inherit Mazur's property from E andF under some conditions. In Section 4, we will also show the stability of Mazur's property under the formation of Schauder decompositions and some unconditional sums of Banach spaces.

scholarly journals Highest-weight vectors in tensor products of Verma modules for U_q(sl_2)

2018 ◽  
Vol 36 (4) ◽  
pp. 107-119 ◽  
Author(s):  
Elizabeth Creath ◽  
Dijana Jakelic
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Alternative Proof ◽  
Verma Modules ◽  
Direct Sums ◽  
Indecomposable Modules ◽  
Enveloping Algebra ◽  
Highest Weight ◽  
Structure Constants ◽  
Quantized Universal Enveloping Algebra

We obtain an explicit basis for the subspace spanned by highest-weight vectors in a tensor product of two highest-weight modules for the quantized universal enveloping algebra of sl_2. The structure constants provide a generalization of the Clebsh-Gordan coefficients. As a byproduct, we give an alternative proof for the decomposition of these tensor products as direct sums of indecomposable modules and supply generators for all highest weight summands.

scholarly journals Extended Weyl-Type Theorems for Direct Sums

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
M. Berkani ◽  
M. Kachad ◽  
H. Zariouh
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Direct Sums ◽  
Bounded Linear ◽  
Direct Sum ◽  
Weyl Type Theorems ◽  
The Stability

AbstractIn this paper, we study the stability of extended Weyl and Browdertype theorems for orthogonal direct sum S⊕T, where S and T are bounded linear operators acting on Banach space. Two counterexamples shows that property (ab), in general, is not preserved under direct sum. Nonetheless, and under the assumptions that Π

scholarly journals Lipschitz (q, p, E)-summing operators on injective Lipschitz tensor products of spaces

2020 ◽  
Vol 6 (1) ◽  
pp. 127-142
Author(s):  
Abdelhamid Tallab
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Product Space ◽  
Tensor Products ◽  
Injective Tensor Product ◽  
Mixing Operators ◽  
Tensor Product Space ◽  
Special Case

AbstractIn this paper, we introduce the notion of (q, p)-mixing operators from the injective tensor product space E ̂⊗∈F into a Banach space G which we call (q, p, F)-mixing. In particular, we extend the notion of (q, p, E)-summing operators which is a special case of (q, p, F)-mixing operators to Lipschitz case by studying their properties and showing some results for this notion.

scholarly journals Properties (V) and (wV) in Projective Tensor Products

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ioana Ghenciu
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Sufficient Conditions ◽  
Tensor Products ◽  
Weakly Compact ◽  
Projective Tensor Product ◽  
Projective Tensor

We give sufficient conditions for a subset of K(X,Y*)=L(X,Y*) to be relatively weakly compact. A Banach space X has property (V) (resp., (wV)) if every V-subset of X* is relatively weakly compact (resp., weakly precompact). We prove that the projective tensor product X⊗πY has property (V) (resp., (wV)), when X has property (V) (resp., (wV)), Y has property (V), and W(X,Y*)=K(X,Y*).

scholarly journals Semicontinuous functions and convex sets in C(K) spaces

2007 ◽  
Vol 82 (1) ◽  
pp. 111-121 ◽  
Author(s):  
J. P. Moreno
Keyword(s):  
Banach Space ◽  
Compact Space ◽  
Convex Sets ◽  
Minkowski Addition ◽  
Stability Properties ◽  
Compact Spaces ◽  
The Family ◽  
The Stability ◽  
Open Question ◽  
Semicontinuous Functions

AbstractThe stability properties of the family ℳ of all intersections of closed balls are investigated in spaces C(K), where K is an arbitrary Hausdorff compact space. We prove that ℳ is stable under Minkowski addition if and only if K is extremally disconnected. In contrast to this, we show that ℳ is always ball stable in these spaces. Finally, we present a Banach space (indeed a subspace of C[0, 1]) which fails to be ball stable, answering an open question. Our results rest on the study of semicontinuous functions in Hausdorff compact spaces.

scholarly journals Fusion frames and g-frames in tensor product and direct sum of Hilbert spaces

2012 ◽  
Vol 6 (2) ◽  
pp. 287-303
Author(s):  
Amir Khosravi ◽  
Azandaryani Mirzaee
Keyword(s):  
Tensor Product ◽  
Finite Number ◽  
Hilbert Spaces ◽  
Product Space ◽  
Tensor Products ◽  
Riesz Bases ◽  
Direct Sums ◽  
Fusion Frames ◽  
Direct Sum ◽  
Tensor Product Space

In this paper we study fusion frames and g-frames for the tensor products and direct sums of Hilbert spaces. We show that the tensor product of a finite number of g-frames (resp. fusion frames, g-Riesz bases) is a g-frame (resp. fusion frame, g-Riesz basis) for the tensor product space and vice versa. Moreover we obtain some important results in tensor products and direct sums of g-frames, fusion frames, resolutions of the identity and duals.

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