THE KAPLAN EXTENSION OF THE RING AND BANACH ALGEBRA OF CONTINUOUS FUNCTIONS AS A DIVISIBLE HULL

1995 ◽  
Vol 45 (3) ◽  
pp. 477-493
Author(s):  
V K Zakharov
Keyword(s):  
Banach Algebra ◽  
Continuous Functions ◽  
Divisible Hull

Convergence Factors and Compactness in Weighted Convolution Algebras

2002 ◽  
Vol 54 (2) ◽  
pp. 303-323 ◽  
Author(s):  
Fereidoun Ghahramani ◽  
Sandy Grabiner
Keyword(s):  
Banach Algebra ◽  
Compact Operator ◽  
Dual Space ◽  
Weighted Space ◽  
Continuous Functions ◽  
Norm Convergence ◽  
Convergence Factor ◽  
Space Of Continuous Functions ◽  
Related Space ◽  
Convolution Algebras

AbstractWe study convergence in weighted convolution algebras L1(ω) on R+, with the weights chosen such that the corresponding weighted space M(ω) of measures is also a Banach algebra and is the dual space of a natural related space of continuous functions. We determine convergence factor ɳ for which weak*-convergence of {λn} to λ in M(ω) implies norm convergence of λn * f to λ * f in L1(ωɳ). We find necessary and sufficent conditions which depend on ω and f and also find necessary and sufficent conditions for ɳ to be a convergence factor for all L1(ω) and all f in L1(ω). We also give some applications to the structure of weighted convolution algebras. As a preliminary result we observe that ɳ is a convergence factor for ω and f if and only if convolution by f is a compact operator from M(ω) (or L1(ω)) to L1(ωɳ).

scholarly journals Some Inequalities arising from a Banach algebra norm

1983 ◽  
Vol 34 (2) ◽  
pp. 199-202 ◽  
Author(s):  
A. M. Russell
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Continuous Functions ◽  
Norm Inequality ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous

AbstractWe derive some specific inequalities involving absolutely continuous functions and relate them to a norm inequality arising from Banach algebras of functions having bounded k th variation.

Functionals on Real C(S)

1978 ◽  
Vol 30 (03) ◽  
pp. 490-498 ◽  
Author(s):  
Nicholas Farnum ◽  
Robert Whitley
Keyword(s):  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Linear Functional ◽  
Hausdorff Space ◽  
Function Algebra ◽  
Continuous Functions ◽  
Codimension One ◽  
Maximal Ideals ◽  
Invertible Elements ◽  
Complex Valued

The maximal ideals in a commutative Banach algebra with identity have been elegantly characterized [5; 6] as those subspaces of codimension one which do not contain invertible elements. Also, see [1]. For a function algebra A, a closed separating subalgebra with constants of the algebra of complex-valued continuous functions on the spectrum of A, a compact Hausdorff space, this characterization can be restated: Let F be a linear functional on A with the property: (*) For each ƒ in A there is a point s, which may depend on f, for which F(f) = f(s).

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.

scholarly journals On Cauchy-type functional equations

2004 ◽  
Vol 2004 (16) ◽  
pp. 847-859
Author(s):  
Elqorachi Elhoucien ◽  
Mohamed Akkouchi
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Functional Equations ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Cauchy Type ◽  
Matrix Functions ◽  
Continuous Solutions ◽  
Locally Compact

LetGbe a Hausdorff topological locally compact group. LetM(G)denote the Banach algebra of all complex and bounded measures onG. For all integersn≥1and allμ∈M(G), we consider the functional equations∫Gf(xty)dμ(t)=∑i=1ngi(x)hi(y),x,y∈G, where the functionsf,{gi},{hi}:G→ℂto be determined are bounded and continuous functions onG. We show how the solutions of these equations are closely related to the solutions of theμ-spherical matrix functions. WhenGis a compact group andμis a Gelfand measure, we give the set of continuous solutions of these equations.

scholarly journals Functional Space C(ω), C0(ω)

2012 ◽  
Vol 20 (1) ◽  
pp. 15-22
Author(s):  
Katuhiko Kanazashi ◽  
Hiroyuki Okazaki ◽  
Yasunari Shidama
Keyword(s):  
Topological Space ◽  
Banach Algebra ◽  
Function Space ◽  
Normed Space ◽  
Functional Space ◽  
Continuous Functions ◽  
Bounded Support ◽  
Compact Topological Space ◽  
Definition Of ◽  
Complex Valued

Functional Space C(ω), C0(ω) In this article, first we give a definition of a functional space which is constructed from all complex-valued continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.

scholarly journals Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support

2010 ◽  
Vol 18 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Katuhiko Kanazashi ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Topological Space ◽  
Banach Algebra ◽  
Function Space ◽  
Functional Space ◽  
Continuous Functions ◽  
Bounded Support ◽  
Compact Topological Space ◽  
Real Normed Space ◽  
Definition Of ◽  
Continuous Functionals

Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all real-valued continuous functions with bounded support. We prove that this function space is a real normed space.

An additivity formula for the strict global dimension of C(Ω)

2014 ◽  
Vol 12 (3) ◽  
Author(s):  
Seytek Tabaldyev
Keyword(s):  
Topological Space ◽  
Tensor Product ◽  
Banach Algebra ◽  
Continuous Functions ◽  
Global Dimension ◽  
Large Cardinality ◽  
The One ◽  
One Point Compactification

AbstractLet A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .

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