منابع مشابه
Approximate Isometries on Finite-dimensional Normed Spaces
Every ε-isometry u between real normed spaces of the same finite dimension which maps the origin to the origin may by uniformly approximated to within 2ε by a linear isometry. Under a smoothness hypothesis, necessary and sufficient conditions are obtained for the same conclusion to hold for a given ε-isometry between infinite-dimensional Banach spaces.
متن کاملIsometries and Approximate Isometries
Some properties of isometric mappings as well as approximate isometries are studied. 2000 Mathematics Subject Classification. Primary 46B04. 1. Isometry and linearity. Mazur and Ulam [17] proved the following well-known result concerning isometries, that is, transformations which preserve distances. Theorem 1.1. Given two real normed vector spaces X and Y , let U be a surjective mapping from X ...
متن کاملApproximate Isometries on Finite Dimensional Banach Spaces by Richard
A map T: Ej —► E2 (E|, E2 Banach spaces) is an e-isometry if III T(X) T(Y)\\ \\X Y\\ I < e whenever X, Ye Ex. The problem of uniformly approximating such maps by isometries was first raised by Hyers and Ulam in 1945 and subsequently studied for special infinite dimensional Banach spaces. This question is here broached for the class of finite dimensional Banach spaces. The only positive homogene...
متن کاملApproximate isometries in Hilbert C ∗ - modules ∗
We use the fixed point alternative theorem to prove that, under suitable conditions, every A-valued approximate isometry on a Hilbert C∗-module over the C∗-algebra A can be approximated by a unique A-valued isometry. AMS subject classifications: Primary 39B52, 39B82, 46B04, 46L08; Secondary 47H10
متن کاملBounded Approximate Character Amenability of Banach Algebras
The bounded approximate version of $varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded ap...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1951
ISSN: 0002-9939
DOI: 10.2307/2032071