Gleason parts and Choquet boundary of a function algebra on a convex compactum

1983 ◽  
Vol 22 (6) ◽  
pp. 1832-1834
Author(s):  
E. L. Arenson
Keyword(s):  
Function Algebra ◽  
Choquet Boundary ◽  
Convex Compactum

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.

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.

scholarly journals A note on the Choquet boundary of a restricted function algebra

1966 ◽  
Vol 18 (3) ◽  
pp. 316-317
Author(s):  
Nozomu Mochizuki
Keyword(s):  
Function Algebra ◽  
Choquet Boundary

Heat equation with singular potential and singular data

2005 ◽  
Vol 135 (4) ◽  
pp. 863-886 ◽  
Author(s):  
M. Nedeljkov ◽  
S. Pilipović ◽  
D. Rajter-Ćirić
Keyword(s):  
Polynomial Growth ◽  
Singular Potential ◽  
Function Algebra ◽  
Energy Estimates ◽  
Generalized Function ◽  
Type Condition ◽  
Classical Energy ◽  
The Cauchy Problem ◽  
White Noise Calculus ◽  
Singular Data

Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.

Boundaries for a Real Function Algebra

2020 ◽  
pp. 136-163
Author(s):  
S. H. Kulkarni ◽  
B.V. Limaye
Keyword(s):  
Real Function ◽  
Function Algebra ◽  
Real Function Algebra

Gleason Parts of a Real Function Algebra

2020 ◽  
pp. 89-135
Author(s):  
S. H. Kulkarni ◽  
B.V. Limaye
Keyword(s):  
Real Function ◽  
Function Algebra ◽  
Real Function Algebra

scholarly journals Remarks on moduli of invertible elements in a function algebra

1974 ◽  
Vol 50 (2) ◽  
pp. 130-132 ◽  
Author(s):  
Junzo Wada
Keyword(s):  
Function Algebra ◽  
Invertible Elements

scholarly journals Dual Algebras and A-Measures

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Marek Kosiek ◽  
Krzysztof Rudol
Keyword(s):  
Analytic Functions ◽  
Complete Solution ◽  
Holomorphic Functions ◽  
Classical Case ◽  
Function Algebra ◽  
Domain Of Holomorphy ◽  
Strict Pseudoconvexity ◽  
Weak Star ◽  
Spectrum Of A Function ◽  
Bounded Holomorphic

Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphyΩ⊂Cn, our approach avoids the use of integral formulae for analytic functions, strict pseudoconvexity, or some other regularity ofΩ. We also investigate the relation between the algebra of bounded holomorphic functions onΩand its abstract counterpart—thew* closure of a function algebraAin the dual of the band of measures generated by one of Gleason parts of the spectrum ofA.

Function algebra methods

1968 ◽  
pp. 117-129
Author(s):  
Lawrence Zalcman
Keyword(s):  
Function Algebra
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