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 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 On the Perron-Frobenius Theory of Mv-matrices and equivalent properties to eventually exponentially nonnegative matrices

2019 ◽  
Vol 35 ◽  
pp. 424-440
Author(s):  
Thaniporn Chaysri ◽  
Dimitrios Noutsos
Keyword(s):  
Necessary Conditions ◽  
Nonnegative Matrix ◽  
Nonnegative Matrices ◽  
Numerical Examples ◽  
Generalized Eigenvectors ◽  
Sufficient And Necessary Conditions ◽  
Left And Right ◽  
Equivalent Properties

Mv−matrix is a matrix of the form A = sI −B, where 0 ≤ ρ(B) ≤ s and B is an eventually nonnegative matrix. In this paper, Mv−matrices concerning the Perron-Frobenius theory are studied. Specifically, sufficient and necessary conditions for an Mv−matrix to have positive left and right eigenvectors corresponding to its eigenvalue with smallest real part without considering or not if index0B ≤ 1 are stated and proven. Moreover, analogous conditions for eventually nonnegative matrices or Mv−matrices to have all the non Perron eigenvectors or generalized eigenvectors not being nonnegative are studied. Then, equivalent properties of eventually exponentially nonnegative matrices and Mv−matrices are presented.  Various numerical examples are given to support our theoretical findings.

scholarly journals Rudin synthesis on homogeneous Banach algebras

1980 ◽  
Vol 29 (4) ◽  
pp. 407-416
Author(s):  
Rong-Song Jih ◽  
Hwai-Chiuan Wang
Keyword(s):  
Banach Algebra ◽  
Necessary Conditions ◽  
Banach Algebras ◽  
Closed Ideal ◽  
Closed Subalgebra ◽  
Sufficient And Necessary Conditions ◽  
Definition Of ◽  
Closed Subalgebras

AbstractThe main results of this article are (I) Let B be a homogeneous Banach algebra, A a closed subalgebra of B, and I the largest closed ideal of B contained in A. We assert that for some closed subalgebra J of B. Furthermore, under suitable conditions, we show that A is an R-subalgebra if and only if J is an R-subalgebra. A number of concrete closed subalgebras of a homogeneous Banach algebra therefore are R-subalgebras. For the definition of P(A) and that of an R-subalgebra, see the introduction in Section 1. (II) We give sufficient and necessary conditions for a closed subalgebra of Lp(G), 1 ≦ p ≦ ∞, to be an R-subalgebra.

scholarly journals Bounded Approximate Identities in Ternary Banach Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Madjid Eshaghi Gordji ◽  
Ali Jabbari ◽  
Gwang Hui Kim
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Approximate Identity ◽  
Approximate Identities ◽  
Left And Right

LetAbe a ternary Banach algebra. We prove that ifAhas a left-bounded approximating set, thenAhas a left-bounded approximate identity. Moreover, we show that ifAhas bounded left and right approximate identities, thenAhas a bounded approximate identity. Hence, we prove Altman’s Theorem and Dixon’s Theorem for ternary Banach algebras.

Biprojectivity and biflatness of amalgamated duplication of Banach algebras

2019 ◽  
Vol 19 (07) ◽  
pp. 2050132
Author(s):  
Ali Ebadian ◽  
Ali Jabbari
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Module Amenability ◽  
Amalgamated Duplication ◽  
Left And Right

Let [Formula: see text] and [Formula: see text] be two Banach 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]. Let [Formula: see text] be a strongly splitting Banach algebra extension of [Formula: see text] by [Formula: see text]. We show that (super) amenability of [Formula: see text] implies (super) module amenability of [Formula: see text] and (super) amenability [Formula: see text]. We investigate biprojectivity and biflatness of [Formula: see text] in the some especial cases. We also give some results related to module biprojectivity and module biflatness of [Formula: see text], when [Formula: see text] is biprojective or biflat.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

Perfect colorings of patterns with multiple orbits

2019 ◽  
Vol 75 (6) ◽  
pp. 814-826
Author(s):  
Allan Junio ◽  
Ma. Lailani Walo
Keyword(s):  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

This paper studies colorings of patterns with multiple orbits, particularly those colorings where the orbits share colors. The main problem is determining when such colorings become perfect. This problem is attacked by characterizing all perfect colorings of patterns through the construction of sufficient and necessary conditions for a coloring to be perfect. These results are then applied on symmetrical objects to construct both perfect and non-perfect colorings.

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