منابع مشابه
Isometries 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 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 کاملApproximate 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 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 کاملOn Galilean Isometries
Quite recently, Carter and Khalatnikov [CK] have pointed out that a geometric fourdimensional formulation of the non relativistic Landau theory of perfect superfluid dynamics should involve not only Galilei covariance but also, more significantly as far as gravitational effects are concerned, covariance under a larger symmetry group which they call the Milne group after Milne’s pioneering work ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1946
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1946-08638-3