scholarly journals On bounded dual-valued derivations on certain Banach algebras

2009 ◽  
Vol 86 (100) ◽  
pp. 107-114
Author(s):  
A.L. Barrenechea ◽  
C.C. Peña
Keyword(s):  
Banach Algebra ◽  
Dual Space ◽  
Banach Algebras ◽  
Class D ◽  
Unitary Dual ◽  
Dual Banach Algebra

We consider the class D(U) of bounded derivations Ud?U*defined on a Banach algebra U with values in its dual space U*so that ?x,d(x)? = 0 for all x?U U. The existence of such derivations is shown, but lacking the simplest structure of an inner one. We characterize the elements of D(U) if span(U2) is dense in U or if U is a unitary dual Banach algebra.

scholarly journals Arens Regularity of Certain Class of Banach Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Abbas Sahleh ◽  
Abbas Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Dual Space ◽  
Banach Algebras ◽  
Arens Regularity ◽  
Left And Right ◽  
Module Extension

We study Arens regularity of the left and right module actions of on , where is thenth dual space of a Banach algebra , and then investigate (quotient) Arens regularity of as a module extension of Banach algebras.

Banach algebras and absolutely summing operators

1976 ◽  
Vol 80 (3) ◽  
pp. 465-473 ◽  
Author(s):  
Andrew M. Tonge
Keyword(s):  
Banach Algebra ◽  
Operator Algebra ◽  
Dual Space ◽  
Banach Algebras ◽  
Uniform Algebra ◽  
Bounded Linear ◽  
Linear Map ◽  
Absolutely Summing Operators ◽  
Image Position

If R is a Banach algebra and ø ∈ R′, the dual space, then we may define a bounded linear map byWe shall show that for suitable p the requirement that each be p-absolutely summing constrains R to be an operator algebra, or even, in certain cases, a uniform algebra. In this way we are able to give generalizations of results of Varopoulos (12) and Kaijser (4).

scholarly journals A generalization on character Connes-amenability

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4059-4070
Author(s):  
Behrouz Shojaee
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Continuous Homomorphism ◽  
Current Paper ◽  
Hereditary Properties ◽  
Connes Amenability ◽  
Dual Banach Algebra

In the current paper, we introduce the concepts of left ?-approximate Connes-amenability and left character approximate Connes-amenability of a dual Banach algebra A that ? is a ?*-continuous homomorphism fromAto C. We also characterize left ?-approximate Connes-amenability ofAin terms of certain derivations and study some hereditary properties for such Banach algebras. Some examples show that these new notions are different from approximate Connes-amenability and left character Connesamenability for dual Banach algebras.

ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS

2021 ◽  
pp. 1-12
Author(s):  
PRAKASH A. DABHI ◽  
DARSHANA B. LIKHADA
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Discrete Groups ◽  
Discrete Semigroups ◽  
Beurling Algebras

Abstract Let $(G_1,\omega _1)$ and $(G_2,\omega _2)$ be weighted discrete groups and $0\lt p\leq 1$ . We characterise biseparating bicontinuous algebra isomorphisms on the p-Banach algebra $\ell ^p(G_1,\omega _1)$ . We also characterise bipositive and isometric algebra isomorphisms between the p-Banach algebras $\ell ^p(G_1,\omega _1)$ and $\ell ^p(G_2,\omega _2)$ and isometric algebra isomorphisms between $\ell ^p(S_1,\omega _1)$ and $\ell ^p(S_2,\omega _2)$ , where $(S_1,\omega _1)$ and $(S_2,\omega _2)$ are weighted discrete semigroups.

A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras

2018 ◽  
Vol 11 (02) ◽  
pp. 1850021 ◽  
Author(s):  
A. Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms ◽  
Unital Banach Algebra

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

scholarly journals Compact linear operators from an algebraic standpoint

1967 ◽  
Vol 8 (1) ◽  
pp. 41-49 ◽  
Author(s):  
F. F. Bonsall
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Linear Operators ◽  
Identity Operator ◽  
Algebra Structure ◽  
Natural Setting ◽  
Norm Topology ◽  
Bounded Linear ◽  
Underlying Space ◽  
Closed Subalgebra

Let B(X) denote the Banach algebra of all bounded linear operators on a Banach space X. Let t be an element of B(X), and let edenote the identity operator on X. Since the earliest days of the theory of Banach algebras, ithas been understood that the natural setting within which to study spectral properties of t is the Banach algebra B(X), or perhaps a closed subalgebra of B(X) containing t and e. The effective application of this method to a given class of operators depends upon first translating the data into terms involving only the Banach algebra structure of B(X) without reference to the underlying space X. In particular, the appropriate topology is the norm topology in B(X) given by the usual operator norm. Theorem 1 carries out this translation for the class of compact operators t. It is proved that if t is compact, then multiplication by t is a compact linear operator on the closed subalgebra of B(X) consisting of operators that commute with t.

Amalgamated duplication of the Banach algebra 𝔄 along a 𝔄-bimodule 𝒜

2018 ◽  
Vol 17 (09) ◽  
pp. 1850169 ◽  
Author(s):  
Hossein Javanshiri ◽  
Mehdi Nemati
Keyword(s):  
Banach Algebra ◽  
Cohomology Group ◽  
Banach Algebras ◽  
Multiplier Algebra ◽  
Topological Center ◽  
Maximal Ideals ◽  
Open Questions ◽  
Arens Regularity ◽  
Amalgamated Duplication

Let [Formula: see text] and [Formula: see text] be Banach algebras such that [Formula: see text] is a Banach [Formula: see text]-bimodule with compatible actions. We define the product [Formula: see text], which is a strongly splitting Banach algebra extension of [Formula: see text] by [Formula: see text]. After characterization of the multiplier algebra, topological center, (maximal) ideals and spectrum of [Formula: see text], we restrict our investigation to the study of semisimplicity, regularity, Arens regularity of [Formula: see text] in relation to that of the algebras [Formula: see text], [Formula: see text] and the action of [Formula: see text] on [Formula: see text]. We also compute the first cohomology group [Formula: see text] for all [Formula: see text] as well as the first-order cyclic cohomology group [Formula: see text], where [Formula: see text] is the [Formula: see text]th dual space of [Formula: see text] when [Formula: see text] and [Formula: see text] itself when [Formula: see text]. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for Lau products and module extensions of Banach algebras as well as triangular Banach algebra. Finally, special attention is devoted to the cyclic and [Formula: see text]-weak amenability of [Formula: see text]. In this context, several open questions arise.

scholarly journals Tensor Products of Banach Algebras

1959 ◽  
Vol 11 ◽  
pp. 297-310 ◽  
Author(s):  
Bernard R. Gelbaum
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Banach Algebras ◽  
Cartesian Product ◽  
Commutative Banach Algebra ◽  
Maximal Ideal Space ◽  
Locally Compact Abelian Group ◽  
Ideal Space ◽  
Integrable Functions ◽  
Group A

This paper is concerned with a generalization of some recent theorems of Hausner (1) and Johnson (4; 5). Their result can be summarized as follows: Let G be a locally compact abelian group, A a commutative Banach algebra, B1 = Bl(G,A) the (commutative Banach) algebra of A-valued, Bochner integrable junctions on G, 3m1the maximal ideal space of A, m2the maximal ideal space of L1(G) [the [commutative Banach] algebra of complex-valued, Haar integrable functions on G, m3the maximal ideal space of B1. Then m3and the Cartesian product m1 X m2are homeomorphic when the spaces mi, i = 1, 2, 3, are given their weak* topologies. Furthermore, the association between m3and m1 X m2is such as to permit a description of any epimorphism E3: B1 → B1/m3 in terms of related epimorphisms E1: A → A/M1 and E2:L1(G) → Ll(G)/M2, where M1 is in mi i = 1, 2, 3.

ONE FUNCTIONAL OPERATOR INVERSION FORMULA

2001 ◽  
Vol 6 (1) ◽  
pp. 138-146 ◽  
Author(s):  
P. Plaschinsky
Keyword(s):  
Banach Algebra ◽  
Explicit Form ◽  
Maximal Ideal ◽  
Inversion Formula ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Functional Operator ◽  
Inversion Operator ◽  
Commutative Banach Algebras ◽  
Algebra Theory

Some results about inversion formula of functional operator with generalized dilation are given. By means of commutative Banach algebra theory the explicit form of inversion operator is expressed. Some commutative Banach algebras with countable generator systems are constructed, their maximal ideal spaces are investigated.

scholarly journals Banach Algebras Which are a Direct Sum of Division Algebras

1988 ◽  
Vol 44 (2) ◽  
pp. 143-145
Author(s):  
Antonio Fernandez Lopez ◽  
Eulalia Garcia Rus
Keyword(s):  
Finite Number ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Division Algebras ◽  
Direct Sum

AbstractIn this note it is proved that a (real or complex) semiprime Banach algebra A satisfying xAx = x2Ax2 for every x ∈ A is a direct sum of a finite number of division Banach algebras.

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