A multiplicative Banach-Stone theorem

2015 ◽  
pp. 191-197
Author(s):  
Kristopher Lee
Keyword(s):  
Stone Theorem

The nonarchimedean Banach-Stone theorem

1990 ◽  
pp. 64-79 ◽  
Author(s):  
Jesús Araujo ◽  
J. Martinez-Maurica
Keyword(s):  
Stone Theorem

scholarly journals A Choquet-Deny theorem for affine functions on a Choquet simplex

1969 ◽  
Vol 16 (4) ◽  
pp. 325-327 ◽  
Author(s):  
H. A. Priestley
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Present Note ◽  
Continuous Functions ◽  
Choquet Simplex ◽  
Affine Functions ◽  
Stone Theorem

The closed wedges in C(X) (the space of real continuous functions on a compact Hausdorff space X) which are also inf-lattices have been characterized by Choquet and Deny (2); see also (5). The present note extends their result to certain wedges of affine continuous functions on a Choquet simplex, the generalization being in the same spirit as the generalization of the Kakutani- Stone theorem obtained by Edwards in (4).I should like to thank my supervisor, Dr D. A. Edwards, for suggesting this problem and for his subsequent help. I am also grateful to the referee for correcting several slips.

scholarly journals Isometries of spaces of unbounded continuous functions

2001 ◽  
Vol 63 (3) ◽  
pp. 475-484
Author(s):  
Jesús Araujo ◽  
Krzysztof Jarosz
Keyword(s):  
Banach Spaces ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Compact Sets ◽  
Surjective Isometry ◽  
Bounded Continuous Functions ◽  
Stone Theorem

By the classical Banach-Stone Theorem any surjective isometry between Banach spaces of bounded continuous functions defined on compact sets is given by a homeomorphism of the domains. We prove that the same description applies to isometries of metric spaces of unbounded continuous functions defined on non compact topological spaces.

scholarly journals The Banach–Stone theorem revisited

2008 ◽  
Vol 155 (16) ◽  
pp. 1800-1803 ◽  
Author(s):  
Z. Ercan ◽  
S. Önal
Keyword(s):  
Stone Theorem

scholarly journals Constructing Banaschewski compactification without Dedekind completeness axiom

2004 ◽  
Vol 2004 (69) ◽  
pp. 3799-3816
Author(s):  
S. K. Acharyya ◽  
K. C. Chattopadhyay ◽  
Partha Pratim Ghosh
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Open Problems ◽  
Structure Space ◽  
Ordered Field ◽  
Completeness Axiom ◽  
Dedekind Completeness ◽  
Stone Theorem ◽  
Stone’S Theorem

The main aim of this paper is to provide a construction of the Banaschewski compactification of a zero-dimensional Hausdorff topological space as a structure space of a ring of ordered field-valued continuous functions on the space, and thereby exhibit the independence of the construction from any completeness axiom for an ordered field. In the process of describing this construction we have generalized the classical versions of M. H. Stone's theorem, the Banach-Stone theorem, and the Gelfand-Kolmogoroff theorem. The paper is concluded with a conjecture of a split in the class of all zero-dimensional but not strongly zero-dimensional Hausdorff topological spaces into three classes that are labeled by inequalities between three compactifications ofX, namely, the Stone-Čech compactificationβX, the Banaschewski compactificationβ0X, and the structure space𝔐X,Fof the lattice-ordered commutative ringℭ(X,F)of all continuous functions onXtaking values in the ordered fieldF, equipped with its order topology. Some open problems are also stated.

scholarly journals Spectral integration and spectral theory for non-Archimedean Banach spaces

2002 ◽  
Vol 31 (7) ◽  
pp. 421-442 ◽  
Author(s):  
S. Ludkovsky ◽  
B. Diarra
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Banach Algebras ◽  
Linear Operators ◽  
Spectral Integration ◽  
Different Types ◽  
Commutative Subalgebras ◽  
Continuous Operators ◽  
Stone Theorem ◽  
Continuous Linear Operators

Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.

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