We prove in Theorem 4.1, for example, for compact X and Y , that a linear isometry H between C(X,E) and C(Y,F) is a "Banach-Stone" map if and only if H is "biseparating (i.e, H and H 1 are separating). The Banach-Stone theorems of Jerison and Lau for vector-valued ...
aluedcontinuousfunctions(7(.Y】and(+(¨)alelineaI‘13tisometricthenXand17’arehomeonlol‘phic.Lately.manyvelsionoftheBanachStonetheotelillmvebeen。btailiedindifferentways.Inthispaper,theantherhasresealchedhardaboutiatti<e_、allledBanach—Stonetheorem、andobtainedagood1esult.Itisthefollowingconclusion:...
Banach–Stone theoremLet X, Y be compact Hausdorff spaces and let E, F be both Banach lattices and Riesz algebras. In this paper, the following main result shall be proved: If F has no zero-divisor and there exists a Riesz algebraic isomorphism Φ : C ( X , E ) → C ( Y , F ...
1. Banach-stone theorem for Banach lattice valued continuous functions [J] . Ercan Z, Onal S Proceedings of the American Mathematical Society . 2007,第9期 机译:Banach格值连续函数的Banach-stone定理 2. Banach-Stone Theorem for Quaternion- Valued Continuous Function Spaces [J] . Kawamura ...
Banach-Stone-type theorems for harmonic spaces U. Schirmeier, Erlangen, F.R. of Germany In this lecture we are going to formulate and prove a theorem of Banach-Stone type in the theory of harmonic spaces. By this well-known theorem two compact spaces X and ~ are homeomorphic iff their ...
Banach–Stone theoremHyers–Ulam stability of isometriesLetXandYbe compact Hausdorff spaces and letF:C(X)→C(Y)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{...
摘要: M-structure and the Banach-Stone theorem. Post a Comment. CONTRIBUTORS: Author: Behrends,Ehrhard (b. 1946, d. ---. PUBLISHER: Springer-Verlag (Berlin and New York). SERIES TITLE: YEAR:1979. PUB TYPE: Book (ISBN 0387095330 ). VOLUME/EDITION关键词:Banach...
Some remarks on the proof method developed here to prove our theorem suggest the conjecture that it is in fact very close to the optimal Banach–Stone theorem for C0(K,22)$C_{0}(K, ell _2^2)$ spaces, or in more precise words, the exact value of the Banach–Stone constant of 22$...
In this way, all three versions of the Banach-Stone theorem are unified in an algebraic framework such that different isomorphisms preserve different ideal structures of C(X). 展开 关键词: Banach-Stone theorem separating maps disjointness preserving maps ...
E has the Banach-Stone property if the descriptive as well as the topological conclusions of the Banach-Stone theorem for scalar functions remain valid in the case of isometries of C(X, E) onto C(Y, E). These two properties were first studied by M. Jerison, and it we later shown ...