We show that RIP frames, tight frames satisfying the restricted isometry property, give rise to nearly tight fusion frames which are nearly orthogonal and hence are nearly equi-isoclinic. We also show how to replace parts of the RIP frame with orthonormal sets while maintaining the restricted isometry property.

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

We show that if f : Bn -IRn is an e-quasi-isometry, with e < 1, defined on the unit ball Bn of Rn, then there is an affine isometry h : Bn -Rn with lIf(x) -h(x)|I < Ce(l+logn) where C is a universal constant. This result is sharp.

In [11] and [12] (textbooks for teachers’ training colleges written by B. Pelle) isometry and similarity are defined not in the classical way but as a product. We continue this way of definition refer to the affine transformation and collineation, and study the fundamental theorems of these mappings analogously to those of isometry and similarity. AMS Classification Number: 00A35 (ZDM: G55, G59)

This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic n-space H for n ≥ 4. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and their contrast with the discrete groups of isometry of H. To the memory of Sasha Reznikov

EP elements are important research objects in the ring theory. This paper mainly gives sufficient and necessary conditions for an element a to be element, partial isometry, strongly by using solutions of certain equations.