scholarly journals ARENS REGULARITY OF PROJECTIVE TENSOR PRODUCT

2021 ◽  
pp. 1251
Author(s):  
Mostfa Shams Kojanaghi ◽  
Kazem Haghnejad Azar
Keyword(s):  
Tensor Product ◽  
Banach Algebra ◽  
Necessary Conditions ◽  
Approximate Identity ◽  
Group Algebras ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Arens Regularity ◽  
Sufficient And Necessary Conditions ◽  
Topological Centers

In this paper, we study approximate identity properties, some propositions from Baker, Dales, Lau in general situations and we establish some relationships between the topological centers of module actions and factorization properties with some results in group algebras. We consider under which sufficient and necessary conditions the Banach algebra $A\widehat{\otimes}B$ is Arens regular.

scholarly journals Arens regularity andweakly compact operators

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4993-5002
Author(s):  
Janko Bracic
Keyword(s):  
Tensor Product ◽  
Weak Compactness ◽  
Linear Operators ◽  
Bilinear Operator ◽  
Tensor Operator ◽  
Projective Tensor Product ◽  
Bilinear Operators ◽  
Projective Tensor ◽  
Arens Regularity ◽  
Topological Centers

We explore the relation between Arens regularity of a bilinear operator and the weak compactness of the related linear operators. Since every bilinear operator has natural factorization through the projective tensor product a special attention is given to Arens regularity of the tensor operator. We consider topological centers of a bilinear operator and we present a few results related to bilinear operators which can be approximated by linear operators.

scholarly journals IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C*-ALGEBRAS

2011 ◽  
Vol 91 (2) ◽  
pp. 275-288 ◽  
Author(s):  
RANJANA JAIN ◽  
AJAY KUMAR
Keyword(s):  
Tensor Product ◽  
Banach Algebra ◽  
Operator Space ◽  
Prime Ideals ◽  
Projective Tensor Product ◽  
C Algebras ◽  
Primitive Ideals ◽  
Projective Tensor

AbstractLet A and B be C*-algebras. We prove the slice map conjecture for ideals in the operator space projective tensor product $A \mathbin {\widehat {\otimes }} B$. As an application, a characterization of the prime ideals in the Banach *-algebra $A\mathbin {\widehat {\otimes }} B$ is obtained. In addition, we study the primitive ideals, modular ideals and the maximal modular ideals of $A\mathbin {\widehat {\otimes }} B$. We also show that the Banach *-algebra $A\mathbin {\widehat {\otimes }} B$ possesses the Wiener property and that, for a subhomogeneous C*-algebra A, the Banach * -algebra $A \mathbin {\widehat {\otimes }} B$ is symmetric.

C∗-algebras defined by amalgamated duplication of C∗-algebras

2019 ◽  
pp. 2150019
Author(s):  
Ali Ebadian ◽  
Ali Jabbari
Keyword(s):  
Banach Algebra ◽  
Necessary Conditions ◽  
Approximate Identity ◽  
C Algebras ◽  
Sufficient And Necessary Conditions ◽  
Amalgamated Duplication ◽  
Left And Right

Let [Formula: see text] and [Formula: see text] be two [Formula: see text]-algebras such that [Formula: see text] is a Banach [Formula: see text]-bimodule with the left and right compatible action of [Formula: see text] on [Formula: see text]. We define [Formula: see text] as a [Formula: see text]-algebra, where it is a strongly splitting [Formula: see text]-algebra extension of [Formula: see text] by [Formula: see text]. Normal, self-adjoint, unitary, invertible and projection elements of [Formula: see text] are characterized; sufficient and necessary conditions for existing unit and bounded approximate identity of [Formula: see text] as a Banach algebra and as a [Formula: see text]-algebra are given. We characterize ∗-automorphisms on [Formula: see text] and give some results related to ∗-homomorphisms, ∗-representations and completely bounded maps on this [Formula: see text]-algebra. Also, we have constructed a new Hilbert [Formula: see text]-module [Formula: see text] over [Formula: see text], where [Formula: see text] is a Hilbert [Formula: see text]-module over [Formula: see text] and [Formula: see text] is a Hilbert [Formula: see text]-module over [Formula: see text].

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.

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

scholarly journals ARENS REGULARITY AND STRONG IRREGULARITY OF CERTAIN BILINEAR MAPPINGS

2019 ◽  
pp. 815
Author(s):  
Somayeh Mohammadzadeh ◽  
Sedigheh Barootkoob
Keyword(s):  
Banach Algebra ◽  
Arens Regularity ◽  
Higher Rank ◽  
Topological Centers

In this paper, the relations between the topological centers of bounded bilinear mappings and some of their higher rank adjoints are investigated. Particularly, for a Banach algebra A, some results about the Banach A−modules and Arens regularity and strong Arens irregularity of module actions will be obtained.

Johnson pseudo-contractibility of second duals of certain Banach algebras

2019 ◽  
pp. 2150012
Author(s):  
A. Sahami ◽  
E. Ghaderi ◽  
S. M. Kazemi Torbaghan ◽  
B. Olfatian Gillan
Keyword(s):  
Tensor Product ◽  
Matrix Algebra ◽  
Banach Algebras ◽  
Amenable Group ◽  
Semigroup Algebra ◽  
Archimedean Semigroup ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
The Matrix ◽  
Second Dual

In this paper, we study Johnson pseudo-contractibility of second dual of some Banach algebras. We show that the semigroup algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is a finite amenable group, where [Formula: see text] is an archimedean semigroup. We also show that the matrix algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is finite. We study Johnson pseudo-contractibility of certain projective tensor product second duals Banach algebras.

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