scholarly journals The centraliser of the injective tensor product

1991 ◽  
Vol 44 (3) ◽  
pp. 357-365 ◽  
Author(s):  
Wend Werner
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Product Formula ◽  
Injective Tensor Product ◽  
Image Position

The aim of this note is to obtain an intrinsic product formula for the centraliser of the injective tensor product of a couple of Banach spaces, Z(). More precisely, we are going to prove thatHere, the spaces and depend only on X and Y, respectively, and Xk denotes the topological k-product.A Counterexaple used to demonstrate that the k-product cannot beavoided serves as an answer to a question posed by W. Rueß and D. Werner concerning the behaviour of M-ideals on Y.

scholarly journals Pietsch integral operators defined on injective tensor products of spaces and applications

1997 ◽  
Vol 39 (2) ◽  
pp. 227-230 ◽  
Author(s):  
Dumitru Popa
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Hausdorff Space ◽  
Integral Operators ◽  
Continuous Functions ◽  
Affirmative Answer ◽  
Nuclear Operators ◽  
Injective Tensor Product ◽  
Image Position

AbstractFor X and Y Banach spaces, let X⊗εY, be the injective tensor product. If Z is also a Banach space and U ∊ L(X⊗εY,Z) we consider the operatorWe prove that if U ∊ PI(X⊗εY, Z), then U# ∊ I(X, PI(Y,Z)). This result is then applied in the case of operators defined on the space of all X-valued continuous functions on the compact Hausdorff space T. We obtain also an affirmative answer to a problem of J. Diestel and J. J. Uhl about the RNP property for the space of all nuclear operators; namely if X* and Y have the RNP and Y can be complemented in its bidual, then N(X, Y) has the RNP.

Some Properties of the Injective Tensor Product of Banach Spaces

2007 ◽  
Vol 23 (9) ◽  
pp. 1697-1706
Author(s):  
Xiao Ping Xue ◽  
Yong Jin Li ◽  
Qing Ying Bu
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Injective Tensor Product

scholarly journals k-Smooth Points in Some Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
A. Saleh Hamarsheh
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Equivalence Classes ◽  
Direct Sums ◽  
Injective Tensor Product ◽  
Bochner Space

We characterize thek-smooth points in some Banach spaces. We will deal with injective tensor product, the Bochner spaceL∞(μ,X)of (equivalence classes of)μ-essentially bounded measurableX-valued functions, and direct sums of Banach spaces.

scholarly journals p-representable operators in Banach spaces

1986 ◽  
Vol 9 (4) ◽  
pp. 653-658
Author(s):  
Roshdi Khalil
Keyword(s):  
Tensor Product ◽  
Unit Ball ◽  
Banach Spaces ◽  
Finite Measure ◽  
Injective Tensor Product

LetEandFbe Banach spaces. An operatorT∈L(E,F)is calledp-representable if there exists a finite measureμon the unit ball,B(E*), ofE*and a functiong∈Lq(μ,F),1p+1q=1, such thatTx=∫B(E*)〈x,x*〉g(x*)dμ(x*)for allx∈E. The object of this paper is to investigate the class of allp-representable operators. In particular, it is shown thatp-representable operators form a Banach ideal which is stable under injective tensor product. A characterization via factorization throughLp-spaces is given.

scholarly journals On the projection constants of some topological spaces and some applications

2001 ◽  
Vol 6 (5) ◽  
pp. 299-308 ◽  
Author(s):  
Entisarat El-Shobaky ◽  
Sahar Mohammed Ali ◽  
Wataru Takahashi
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Topological Spaces ◽  
Projective Tensor Product ◽  
Injective Tensor Product ◽  
Lower Estimation ◽  
Projective Tensor ◽  
Projection Constant

We find a lower estimation for the projection constant of the projective tensor productX⊗ ∧Yand the injective tensor productX⊗ ∨Y, we apply this estimation on some previous results, and we also introduce a new concept of the projection constants of operators rather than that defined for Banach spaces.

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 SUBPROJECTIVITY OF PROJECTIVE TENSOR PRODUCTS OF BANACH SPACES OF CONTINUOUS FUNCTIONS

2021 ◽  
pp. 1-14
Author(s):  
R.M. CAUSEY
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Tensor Products ◽  
Continuous Functions ◽  
Hausdorff Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Spaces Of Continuous Functions

Abstract Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces K1, …, K n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each K i is scattered.

The wigner property for CL-spaces and finite-dimensional polyhedral banach spaces

2021 ◽  
pp. 1-17
Author(s):  
Dongni Tan ◽  
Xujian Huang
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Phase Function ◽  
Linear Isometry ◽  
Basic Properties ◽  
Finite Dimensional ◽  
Image Position

Abstract We say that a map $f$ from a Banach space $X$ to another Banach space $Y$ is a phase-isometry if the equality \[ \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \] holds for all $x,\,y\in X$ . A Banach space $X$ is said to have the Wigner property if for any Banach space $Y$ and every surjective phase-isometry $f : X\rightarrow Y$ , there exists a phase function $\varepsilon : X \rightarrow \{-1,\,1\}$ such that $\varepsilon \cdot f$ is a linear isometry. We present some basic properties of phase-isometries between two real Banach spaces. These enable us to show that all finite-dimensional polyhedral Banach spaces and CL-spaces possess the Wigner property.

scholarly journals Completely bounded bimodule maps and spectral synthesis

2017 ◽  
Vol 28 (10) ◽  
pp. 1750067 ◽  
Author(s):  
M. Alaghmandan ◽  
I. G. Todorov ◽  
L. Turowska
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Closed Subset ◽  
Spectral Synthesis ◽  
Locally Compact Group ◽  
Product Formula ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

scholarly journals Types of Radon-Nikodym properties for the projective tensor product of Banach spaces

2003 ◽  
Vol 47 (4) ◽  
pp. 1303-1326 ◽  
Author(s):  
Qingying Bu ◽  
Joe Diestel ◽  
Patrick Dowling ◽  
Eve Oja
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor
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