Stable ranks for the real function algebra $C(X,\tau)$

2011 ◽  
Vol 60 (1) ◽  
pp. 269-284 ◽  
Author(s):  
Raymond Mortini ◽  
Rudolf Rupp
Keyword(s):  
Real Function ◽  
Function Algebra ◽  
The Real ◽  
Real Function Algebra

SEPARATION PROPERTIES AND OPERATING FUNCTIONS ON A SPACE OF CONTINUOUS FUNCTIONS

1993 ◽  
Vol 04 (04) ◽  
pp. 551-600 ◽  
Author(s):  
OSAMU HATORI
Keyword(s):  
Function Space ◽  
Real Function ◽  
Banach Function Space ◽  
Function Algebra ◽  
Continuous Functions ◽  
Positive Answer ◽  
Banach Function Spaces ◽  
The Real ◽  
Affine Functions ◽  
Real Function Algebra

Characterizations of the space CR (X) of all real-valued continuous functions on a compact Hausdorff space X among its subspaces are investigated under the circumstances of operating functions. One of the main purpose in this paper is to disprove the following conjecture: if a non-affine function operates on an ultraseparating real Banach function space E on X, then E = CR (X). A positive answer is given in the case that E satisfies a stronger separation axiom than ultraseparation one, which the real part of an ultraseparating Banach function algebra satisfies. For the original conjecture a counterexample is given; there is an ultraseparating real Banach function space on a compact metric space Y on which the function |·| operates, but it does not coincide with CR (Y). A characterization is given for non-affine functions which operate only on CR (X) among ultraseparating real Banach function spaces on X. By using these results the symbolic calculus on real Banach function spaces is investigated without extra hypothesis of ultraseparation. Several non-local-Lipschitz functions are shown not to operate on a real Banach function space E on X unless E = CR (X). In particular, the function tp defined on [0,1) for a p with 0 < p < 1 or the standard Cantor function on [0, 1] never operates on a real Banach function space E on X unless E = CR (X). Functions which operate on the real part of a real function algebra are also investigated. A positive answer is given for the conjecture that only affine functions operate on the real part of a non-trivial real function algebra.

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

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 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.

Aristóteles Contra o Bem dos Economistas

2021 ◽  
Vol 77 (1) ◽  
pp. 217-234
Author(s):  
Mário Maximo
Keyword(s):  
Economic Theory ◽  
Moral Philosophy ◽  
Real Function ◽  
Capability Approach ◽  
Capabilities Approach ◽  
Ethical Naturalism ◽  
Human Form ◽  
The Real ◽  
Weak Points ◽  
The Capability Approach

Despite its origins within moral philosophy, economists think their science has nothing to do with the good. They appeal to some kind of Hume’s guillotine that divides the descriptive and the normative. With that in hand, they affirm the solely descriptive aspect of their discipline. I argue this is not the case. Economists have, as they need to, an all encompassing notion of the good. I suggest going back to Aristotelian arguments to show the shortcomings of this good of economists. Aristotle is helpful because of his analysis of chrematistics and the real function of money. Hence, the loosely utilitarian good of the economists is confronted with a robust sense of the good and the human form. The capability approach is the first to identify these weak points on economic theory and to propose a sort of Aristotelian comeback. However, I claim the capabilities approach itself doesn’t follow the Aristotelian arguments used to attack economists to its necessary conclusion. Therefore, I suggest that the recent advances in neo-Aristotelian ethical naturalism can be used to reformulate economics by dispossessing economists of their sumo bonnun.

Gleason Parts of Real Function Algebras

1981 ◽  
Vol 33 (1) ◽  
pp. 181-200 ◽  
Author(s):  
S. H. Kulkarni ◽  
B. V. Limaye
Keyword(s):  
Real Function ◽  
Banach Algebras ◽  
Complex Function ◽  
Klein Surfaces ◽  
The Real ◽  
Uniform Algebras ◽  
Function Algebras ◽  
Complex Valued ◽  
Systematic Exposition

Although the theory of complex Banach algebras is by now classical, the first systematic exposition of the theory of real Banach algebras was given by Ingelstam [5] as late as 1965. More recently, further attention to real Banach algebras was paid in 1970 [1], where, among other things, the (real) standard algebras on finite open Klein surfaces were introduced. Generalizing these considerations, real uniform algebras were studied in [7] and [6].In the present paper, an attempt is made to develop the theory of real function algebras (see Section 1 for the definition) along the lines of the complex function algebras. Although the real function algebras are not structurally different from the real uniform algebras introduced in [7], they are easier to deal with since their elements are actually (complex-valued) functions.

Sign in / Sign up

Export Citation Format

Share Document