The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of C0(R) ⊗ B(H) is an automorphism, respectively a surjective isometry.

We extend Witt’s theorem to several kinds of simultaneous isometries of subspaces. We determine sufficient and necessary conditions for the extension of an isometry of subspaces φ : E → E′ to an isometry φV : V → V ′ that also sends a given subspace to another, or a given self-dual flag to another, or a Witt’s decomposition to another and a special self-dual flag to another. We also determine s...

In low dimensional gravity on anti-de sitter space there exists a possibility that the asymptotic isometry is raised to a Virasoro symmetry living at spatial infinity. We discuss in detail asymptotic isometry of the most general anti-de sitter dilaton gravity in two dimensions. From analysis of the boundary dynamics it turns out that the Virasoro symmetry is not preserved in all the models. Mor...

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.

A finite set W ⊂ R is said to realize the group G if the isometry group of W is isomorphic to G. The isometry dimension of a group is the minimum dimension of a realization. It is known that the isometry dimension of G is less than |G| [1]. We show that the isometry dimension of Z2 is n. The orbit number of a group is the minimum number of orbits in a realization. We show that the groups Z2 are...

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...

We explore the structure of compact Riemann surfaces by studying their isometry groups. First we give two constructions due to Accola [1] showing that for all g ≥ 2, there are Riemann surfaces of genus g that admit isometry groups of at least some minimal size. Then we prove a theorem of Hurwitz giving an upper bound on the size of any isometry group acting on any Riemann surface of genus g ≥ 2...

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...