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.

scholarly journals PROPERTIES OF CERTAIN SUBALGEBRAS OF DALES-DAVIE ALGEBRAS

2007 ◽  
Vol 49 (2) ◽  
pp. 225-233 ◽  
Author(s):  
M. ABTAHI ◽  
T. G. HONARY
Keyword(s):  
Maximal Ideal ◽  
Rational Functions ◽  
Maximal Ideal Space ◽  
Analytic Extension ◽  
Ideal Space ◽  
Differentiable Functions ◽  
Function Algebras ◽  
Infinitely Differentiable Functions ◽  
Interesting Class ◽  
Compact Plane

AbstractWe study an interesting class of Banach function algebras of infinitely differentiable functions on perfect, compact plane sets. These algebras were introduced by H. G. Dales and A. M. Davie in 1973, called Dales-Davie algebras and denoted by D(X, M), where X is a perfect, compact plane set and M = {Mn}∞n = 0 is a sequence of positive numbers such that M0 = 1 and (m + n)!/Mm+n ≤ (m!/Mm)(n!/Mn) for m, n ∈ N. Let d = lim sup(n!/Mn)1/n and Xd = {z ∈ C : dist(z, X) ≤ d}. We show that, under certain conditions on X, every f ∈ D(X, M) has an analytic extension to Xd. Let DP [DR]) be the subalgebra of all f ∈ D(X, M) that can be approximated by the restriction to X of polynomials [rational functions with poles off X]. We show that the maximal ideal space of DP is $X^_d$, the polynomial convex hull of Xd, and the maximal ideal space of DR is Xd. Using some formulae from combinatorial analysis, we find the maximal ideal space of certain subalgebras of Dales-Davie algebras.

The Maximal Ideal Space of Subalgebras of the Disk Algebra

1975 ◽  
Vol 18 (1) ◽  
pp. 61-65 ◽  
Author(s):  
Bruce Lund
Keyword(s):  
Unit Disk ◽  
Maximal Ideal ◽  
Function Algebra ◽  
Continuous Functions ◽  
Maximal Ideal Space ◽  
Open Unit ◽  
Ideal Space ◽  
Disk Algebra ◽  
Closed Subalgebra ◽  
Uniformly Closed

Let X be a compact Hausdorff space and C(X) the complexvalued continuous functions on X. We say A is a function algebra on X if A is a point separating, uniformly closed subalgebra of C(X) containing the constant functions. Equipped with the sup-norm ‖f‖ = sup{|f(x)|: x ∊ X} for f ∊ A, A is a Banach algebra. Let MA denote the maximal ideal space.Let D be the closed unit disk in C and let U be the open unit disk. We call A(D)={f ∊ C(D):f is analytic on U} the disk algebra. Let T be the unit circle and set C1(T) = {f ∊ C(T): f'(t) ∊ C(T)}.

scholarly journals A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Raymond Mortini ◽  
Rudolf Rupp
Keyword(s):  
Maximal Ideal ◽  
Stable Rank ◽  
Uniform Algebra ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Smooth Functions ◽  
Function Algebras ◽  
Classical Function ◽  
Complex Valued ◽  
Compact Planar

We determine, via classroom proofs, the maximal ideal space, the Bass stable rank as well as the topological and dense stable rank of the uniform closure of all complex-valued functions continuously differentiable on neighborhoods of a compact planar set and holomorphic in the interior of . In this spirit, we also give elementary approaches to the calculation of these stable ranks for some classical function algebras on .

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.

Real linear isometries between function algebras. II

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Osamu Hatori ◽  
Takeshi Miura
Keyword(s):  
Maximal Ideal ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Hausdorff Spaces ◽  
Shilov Boundary ◽  
Locally Compact ◽  
Choquet Boundary ◽  
Function Algebras ◽  
Real Linear ◽  
Uniformly Closed

AbstractWe describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

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.

Sign in / Sign up

Export Citation Format

Share Document