scholarly journals Weakly analytic sets for the Cartesian product of function algebra

10.29007/tsfl ◽  
2018 ◽  
Author(s):  
Himali Mehta ◽  
Rekha Mehta ◽  
Aakar Roghelia
Keyword(s):  
Cartesian Product ◽  
Function Algebra ◽  
Function Algebras ◽  
Analytic Sets

Weakly analytic sets for function algebra is studied by Arenson in (Arenson). Here, we study the concept of weakly analytic sets for Cartesian product of function algebras. We express the weakly analytic sets for Cartesian product of function algebra in terms of that for factor algebras.

Ring Derivations on Function Algebras

1990 ◽  
Vol 33 (1) ◽  
pp. 69-72 ◽  
Author(s):  
N. R. Nandakumar
Keyword(s):  
Function Algebra ◽  
Choquet Boundary ◽  
Function Algebras ◽  
Ring Derivation

AbstractIn this paper we show that a ring derivation on a function algebra is trivial provided that the Choquet boundary of the algebra contains a dense sequentially non-isolated set.

Boundaries for the Cartesian product of real function algebras

2019 ◽  
Author(s):  
H. S. Mehta ◽  
R. D. Mehta ◽  
A. N. Roghelia
Keyword(s):  
Real Function ◽  
Cartesian Product ◽  
Function Algebras

scholarly journals Generalized Numerical Index of Function Algebras

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Han Ju Lee
Keyword(s):  
Banach Space ◽  
Function Algebra ◽  
Complex Banach Space ◽  
Continuous Functions ◽  
Function Algebras ◽  
Bounded Complex ◽  
Closed Subalgebra ◽  
Bounded Continuous Functions ◽  
Complex Valued ◽  
Numerical Index

Let X be a complex Banach space and Cb(Ω:X) be the Banach space of all bounded continuous functions from a Hausdorff space Ω to X, equipped with sup norm. A closed subspace A of Cb(Ω:X) is said to be an X-valued function algebra if it satisfies the following three conditions: (i) A≔{x⁎∘f:f∈A,  x⁎∈X⁎} is a closed subalgebra of Cb(Ω), the Banach space of all bounded complex-valued continuous functions; (ii) ϕ⊗x∈A for all ϕ∈A and x∈X; and (iii) ϕf∈A for every ϕ∈A and for every f∈A. It is shown that k-homogeneous polynomial and analytic numerical index of certain X-valued function algebras are the same as those of X.

Choquet Boundary for Real Function Algebras

1988 ◽  
Vol 40 (5) ◽  
pp. 1084-1104 ◽  
Author(s):  
S. H. Kulkarni ◽  
S. Arundhathi
Keyword(s):  
Real Function ◽  
Complex Function ◽  
Function Algebra ◽  
Shilov Boundary ◽  
Representing Measure ◽  
Continuous Linear Functional ◽  
Choquet Boundary ◽  
Function Algebras ◽  
Real Function Algebra ◽  
Real Algebras

The concepts of Choquet boundary and Shilov boundary are well-established in the context of a complex function algebra (see [2] for example). There have been a few attempts to develop the concept of a Shilov boundary for real algebras, [4], [6] and [7]. But there seems to be none to develop the concept of Choquet boundary for real algebras.The aim of this paper is to develop the theory of Choquet boundary of a real function algebra (see Definition (1.8)) along the lines of the corresponding theory for a complex function algebra.In the first section we define a real-part representing measure for a continuous linear functional ϕ on a real function algebra A with the property ║ϕ║ = 1 = ϕ(1). The elements of A are functions on a compact, Hausdorff space X. The Choquet boundary is then defined as the set of those points x ∊ X such that the real part of the evaluation functional, Re(ex), has a unique real part representing measure.

Maximality In Function Algebras

1970 ◽  
Vol 22 (5) ◽  
pp. 1002-1004 ◽  
Author(s):  
Robert G. Blumenthal
Keyword(s):  
Metric Space ◽  
Hausdorff Space ◽  
Function Algebra ◽  
General Function ◽  
Maximal Subalgebra ◽  
Maximal Subalgebras ◽  
Disc Algebra ◽  
Function Algebras ◽  
Closed Point ◽  
Uniformly Closed

In this paper we prove that the proper Dirichlet subalgebras of the disc algebra discovered by Browder and Wermer [1] are maximal subalgebras of the disc algebra (Theorem 2). We also give an extension to general function algebras of a theorem of Rudin [4] on the existence of maximal subalgebras of C(X). Theorem 1 implies that every function algebra defined on an uncountable metric space has a maximal subalgebra.A function algebra A on X is a uniformly closed, point-separating subalgebra of C(X), containing the constants, where X is a compact Hausdorff space. If A and B are function algebras on X, A ⊂ B, A ≠ B, we say A is a maximal subalgebra of B if whenever C is a function algebra on X with A ⊂ C ⊂ B, either C = A or C = B.

scholarly journals Regular completions of Cauchy spaces via function algebras

1974 ◽  
Vol 11 (1) ◽  
pp. 77-88 ◽  
Author(s):  
R.J. Gazik ◽  
D.C. Kent
Keyword(s):  
Function Algebra ◽  
Universal Property ◽  
Continuous Convergence ◽  
Function Algebras ◽  
Cauchy Space ◽  
Convergence Structure ◽  
Cauchy Spaces

A regular completion with the universal property is obtained for each member of a certain class of Cauchy spaces by embedding the Cauchy space in a complete function algebra with the continuous convergence structure.

scholarly journals Maximal ideal space of function algebras

1997 ◽  
Vol 63 (1) ◽  
pp. 78-90
Author(s):  
Jorge Bustamante González ◽  
Raul Escobedo Conde
Keyword(s):  
Real Function ◽  
Normed Space ◽  
Maximal Ideal ◽  
Function Algebra ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Uniform Spaces ◽  
Differentiable Functions ◽  
Function Algebras ◽  
Real Function Algebra

AbstractWe present a representation theory for the maximal ideal space of a real function algebra, endowed with the Gelfand topology, using the theory of uniform spaces. Application are given to algebras of differentiable functions in a normęd space, improving and generalizing some known results.

A Topological Characterization of Gleason Parts of Real Function Algebras

1983 ◽  
Vol 26 (1) ◽  
pp. 44-49
Author(s):  
S. H. Kulkarni ◽  
B. V. Limaye
Keyword(s):  
Topological Space ◽  
Real Function ◽  
Complex Function ◽  
Function Algebra ◽  
Topological Characterization ◽  
Gleason Part ◽  
Completely Regular ◽  
Compact Topological Space ◽  
Function Algebras ◽  
Real Function Algebra

AbstractIt is well-known that a topological space is a Gleason part of some complex function algebra if and only if it is completely regular and σ-compact. In the present paper, a Gleason part of a real function algebra is characterized as a completely regular σ-compact topological space which admits an involutoric homeomorphism.

scholarly journals Isomorphisms of Function Algebras and Algebras of Analytic Functions

1978 ◽  
Vol 21 (1) ◽  
pp. 61-71
Author(s):  
Bruce Lund
Keyword(s):  
Riemann Surface ◽  
Analytic Functions ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Function Algebra ◽  
Finite Codimension ◽  
Open Riemann Surface ◽  
Analytic Boundary ◽  
Function Algebras

AbstractLet R be a finite open Riemann surface with analytic boundary Γ. Set and define is analytic on R}. Conditions are given on a function algebra A on a compact Hausdorff space X which imply that A is isomorphic to a subalgebra of A(R) of finite codimension.

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