Banach-stone theorem for Banach lattice valued continuous functions

Download

index.pdf

Date

2007-01-01

Author

Ercan, Z.
Onal, S.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

53
views

0
downloads

Let Chi and Upsilon be compact Hausdor spaces, Epsilon be a Banach lattice and F be an AM space with unit. Let pi : C(X, E) -> C(Upsilon, F) be a Riesz isomorphism such that 0 not subset of f (X) if and only if 0 not subset of pi (f)(Upsilon) for each f is an element of C(Chi, Epsilon). We prove that Chi is homeomorphic to Upsilon and Epsilon is Riesz isomorphic to F. This generalizes some known results.

Subject Keywords

Applied Mathematics, General Mathematics

URI

https://hdl.handle.net/11511/65938

Journal

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1090/s0002-9939-07-08788-6

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

A formula for the joint local spectral radius Emel'yanov, EY; Ercan, Z (American Mathematical Society (AMS), 2004-01-01) We give a formula for the joint local spectral radius of a bounded subset of bounded linear operators on a Banach space X in terms of the dual of X.
On homology of real algebraic varieties Ozan, Yıldıray (American Mathematical Society (AMS), 2001-01-01) Let R be a commutative ring with unity and X an R-oriented compact nonsingular real algebraic variety of dimension n. If i : X --> X-C is any nonsingular complexification of X, then the kernel, which we will denote by KHk(X, R), of the induced homomorphism i(*) : H-k(X, R) --> H-k(X-C, R) is independent of the complexification. In this work, we study KHk(X, R) and give some of its applications.
Betti numbers of fixed point sets and multiplicities of indecomposable summands Öztürk, Semra (Cambridge University Press (CUP), 2003-04-01) Let G be a finite group of even order, k be a field of characteristic 2, and M be a finitely generated kG-module. If M is realized by a compact G-Moore space X, then the Betti numbers of the fixed point set X-Cn and the multiplicities of indecomposable summands of M considered as a kC(n)-module are related via a localization theorem in equivariant cohomology, where C-n is a cyclic subgroup of G of order n. Explicit formulas are given for n = 2 and n = 4.
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications Ercan, Z (American Mathematical Society (AMS), 2004-01-01) We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
Holomorphic extension of meromorphic mappings along real analytic hypersurfaces Yazıcı, Özcan (Springer Science and Business Media LLC, 2020-08-01) Let M subset of C-n be a real analytic hypersurface, M' subset of C-N (N >= n) be a strongly pseudoconvex real algebraic hypersurface of the special form, and F be a meromorphic mapping in a neighborhood of a point p is an element of M which is holomorphic in one side of M. Assuming some additional conditions for the mapping F on the hypersurface M, we proved that F has a holomorphic extension to p. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensi...

Citation Formats

Z. Ercan and S. Onal, “Banach-stone theorem for Banach lattice valued continuous functions,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 2827–2829, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65938.