Compact semigroups in commutative Banach algebras

1969 ◽  
Vol 66 (2) ◽  
pp. 265-274 ◽  
Author(s):  
M. A. Kaashoek ◽  
T. T. West
Keyword(s):  
Banach Algebra ◽  
Topological Semigroup ◽  
Spectral Properties ◽  
Banach Algebras ◽  
Structure Theory ◽  
Compact Semigroups ◽  
Commutative Banach Algebras ◽  
Continuous Multiplication ◽  
Natural Way

A monothetic semigroup is a topological semigroup with jointly continuous multiplication which contains a dense cyclic subsemigroup. These semi-groups arise in a natural way in the study of semi-algebras. In (4) we showed that a compact monothetic semigroup in a Banach algebra can be characterized in terms of the spectral properties of a generating element. In this paper these spectral theorems are linked with the well-known structure theory of compact semigroups.

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 Homology and cohomology groups of commutative Banach algebras and analytic polydiscs

2000 ◽  
Vol 42 (1) ◽  
pp. 15-24
Author(s):  
L. I. Pugach ◽  
M. C. White
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Deformation Theory ◽  
Banach Algebras ◽  
Subject Classification ◽  
Analytic Structure ◽  
Homological Dimension ◽  
Cohomology Groups ◽  
Main Method ◽  
Commutative Banach Algebras

In this paper we deduce the existence of analytic structure in a neighbourhood of a maximal ideal M in the spectrum of a commutative Banach algebra, A, from homological assumptions. We assume properties of certain of the cohomology groups H^n(A,A/M), rather than the stronger conditions on the homological dimension of the maximal ideal the first author has considered in previous papers. The conclusion is correspondingly weaker: in the previous work one deduces the existence of a Gel'fand neighbourhood with analytic structure, here we deduce only the existence of a metric neighbourhood with analytic structure. The main method is to consider products of certain co-cycles to deduce facts about the symmetric second cohomology, which is known to be related to the deformation theory of algebras.1991 Mathematics Subject Classification. 46J20, 46M20.

scholarly journals Spectral properties of elements in different Banach algebras

1991 ◽  
Vol 33 (1) ◽  
pp. 11-20 ◽  
Author(s):  
J. J. Grobler ◽  
H. Raubenheimer
Keyword(s):  
Banach Algebra ◽  
Spectral Properties ◽  
Banach Algebras ◽  
Sufficient Conditions

Let A be a Banach algebra with unit 1 and let B be a Banach algebra which is a subalgebra of A and which contains 1. In [5]Barnes gave sufficient conditions for B to be inverse closed in A. In this paper we consider single elements and study the question of how the spectrum relative to B of an element in B relates to the spectrum of the element relative to A.

scholarly journals Similarité entre l'algèbre de Volterra et un quotient d'algèbre uniforme

1991 ◽  
Vol 34 (3) ◽  
pp. 383-391 ◽  
Author(s):  
Konin Koua
Keyword(s):  
Banach Algebra ◽  
Half Plane ◽  
Banach Algebras ◽  
Continuous Functions ◽  
Compact Mapping ◽  
Dense Ideal ◽  
Right Hand ◽  
Commutative Banach Algebras ◽  
One To One

Two commutative Banach algebras A and B are said to be similar if there exists a Banach algebra D such that [xD]− = D for some x in D, and two one-to-one continuous homomorphisms φ:D→A and ψ:D→B such that φ(D) is a dense ideal of A and ψ(D) a dense ideal of B.We prove in this paper that the Volterra algebra is similar to A0/e-z A0 where A0 is the commutative uniform, separable Banach algebra of all continuous functions on the closed right-hand half plane , analytic on H and vanishing at infinity. We deduce from this result that multiplication by an element of A0/e-z A0 is a compact mapping.

Representation theory for tensor products of Banach algebras

1981 ◽  
Vol 90 (3) ◽  
pp. 445-463 ◽  
Author(s):  
T. K. Carne
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Tensor Products ◽  
The Subject ◽  
Algebraic Tensor Product ◽  
Natural Way

The algebraic tensor product A1⊗A2 of two Banach algebras is an algebra in a natural way. There are certain norms α on this tensor product for which the multiplication is continuous so that the completion, A1αA2, is a Banach algebra. The representation theory of such tensor products is the subject of this paper. It will be shown that, under certain simple conditions, the tensor product of two semi-simple Banach algebras is semi-simple although, without these conditions, the result fails.

Discontinuous homomorphisms from Banach *-algebras

1996 ◽  
Vol 120 (4) ◽  
pp. 703-708
Author(s):  
Volker Runde
Keyword(s):  
Banach Algebra ◽  
Open Problem ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuum Hypothesis ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Commutative Banach Algebras ◽  
The Continuum

The long open problem raised by I. Kaplansky if, for an infinite compact Hausdorff space X, there is a discontinuous homomorphism from (X) into a Banach algebra was settled in the 1970s, independently, by H. G. Dales and J. Esterle. If the continuum hypothesis is assumed, then there is a discontinuous homomorphism from (X) (see [8] for a survey of both approaches and [9] for a unified exposition). The techniques developed by Dales and Esterle are powerful enough to yield discontinuous homomorphisms from commutative Banach algebras other than (X). In fact, every commutative Banach algebra with infinitely many characters is the domain of a discontinuous homomorphism ([7]).

Commutative Banach Algebras with Idempotent Maximal Ideals

1969 ◽  
Vol 9 (3-4) ◽  
pp. 275-286 ◽  
Author(s):  
R. J. Loy
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Complex Field ◽  
Linear Combinations ◽  
Maximal Ideals ◽  
Commutative Banach Algebras ◽  
Finite Linear

Letbe a commutative Banach algebra over the complex fieldC,Man ideal of. Denote byM2the set of all finite linear combinations of products of elements fromM.Mwill be termed idempotent ifM2=M. The purpose of this paper is to investigate the structure of commutative Banach algebras in which all maximal ideals are idempotent.

scholarly journals Higher point derivations on commutative Banach algebras, III

1981 ◽  
Vol 24 (1) ◽  
pp. 31-40 ◽  
Author(s):  
H. G. Dales ◽  
J. P. McClure
Keyword(s):  
Banach Algebra ◽  
Infinite Order ◽  
Infinite Sequence ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Complex Field ◽  
Linear Functionals ◽  
Point Derivation ◽  
Commutative Banach Algebras ◽  
Image Position

Let A be a commutative Banach algebra with identity 1 over the complex field C, and let d0 be a character on A. We recall that a (higher) point derivation of order q on A at d0 is a sequence d1, …, dq of linear functionals on A such that the identitieshold for each choice of f and g in A and k in {1, …, q}. A point derivation of infinite order is an infinite sequence {dk} of linear functionals such that (1.1) holds for all k. A point derivation is continuous if each dk is continuous, totally discontinuous if dk is discontinuous for each k≧1, and degenerate if d1 = 0.

scholarly journals Stability of -Jordan Homomorphisms from a Normed Algebra to a Banach Algebra

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yang-Hi Lee
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Ring Homomorphism ◽  
Normed Algebra ◽  
Jordan Homomorphism ◽  
Commutative Banach Algebras ◽  
Jordan Homomorphisms

We establish the hyperstability of -Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an -Jordan homomorphism between two commutative Banach algebras is an -ring homomorphism.

Sign in / Sign up

Export Citation Format

Share Document