In 1964, Michael Edelstein presented an amazing affine isometry acting on the space of square-summable sequences. This operator has no fixed points, but a suborbit that converges to 0 while another...

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 ...

We prove that Banach spaces ℓ1 ⊕2 R and X ⊕∞ Y , with strictly convex have plastic unit balls (we call a metric space if every non-expansive bijection from this onto itself is an isometry).

We shall begin by recalling some material from quadrics1.pdf, which gave the classification of hyperquadrics in R and C up to affine equivalence: CONGRUENCE OR ISOMETRY CLASSIFICATION PROBLEM. Given two affine hyperquadrics Σ1 and Σ2 in R , is there a congruence or isometry T from R to itself mapping Σ1 onto Σ2? There are two possible versions of the question. An arbitrary isometry T from R to ...

We propose a novel local isometry based dimensionality reduction method from the perspective of vector fields, which is called parallel vector field embedding (PFE). We first give a discussion on local isometry and global isometry to show the intrinsic connection between parallel vector fields and isometry. The problem of finding an isometry turns out to be equivalent to finding orthonormal par...

1 Abstract By using symplectic Majorana spinors as Grassmann coordinates in a superspace associated with the supersymmetric extension of the isometry group on the spherical surface S 2 , it proves possible to formulate supersymmetric models on S 2 using superspace techniques. The formulation of gauge theories on a spherical surface [1] has provided insights into their properties. The kinetic te...

A class of metrics with isometry group SO(2, 1) × SO(2) × ℜ is derived. Gödel solution belongs to it , and is the only case corresponding to the stress-energy tensor of a perfect fluid.

Let V be an n-dimensional vector space over a finite field Fq and P = {1, 2, . . . , n} a poset. We consider on V the poset-metric dP . In this paper, we give a complete description of groups of linear isometries of the metric space (V, dP ), for any poset-metric dP . We show that a linear isometry induces an automorphism of order in poset P , and consequently we show the existence of a pair of...

A set of points W in Euclidean space is said to realize the finite group G if the isometry group of W is isomorphic to G. We show that every finite group G can be realized by a finite subset of some R n, with n < |G|. The minimum dimension of a Euclidean space in which G can be realized is called its isometry dimension. We discuss the isometry dimension of small groups and offer a number of ope...

Abstract. We consider three lifting questions: Given a C∗-algebra I, if there is a unital C∗-algebra A contains I as an ideal, is every unitary from A/I lifted to a unitary in A? is every unitary from A/I lifted to an extremal partial isometry? is every extremal partial isometry from A/I lifted to an extremal partial isometry? We show several constructions of I which serve as working examples o...