Nonsurjective Nearisometries of Banach Spaces

A survey of nearisometries

1.1. Notation. Throughout this article, E and F are real Banach spaces (sometimes Hilbert spaces or just euclidean spaces) of dimension at least one. The norm of a vector x is written as |x|. In a Hilbert space we let x · y denote the inner product of vectors x and y. Open and closed balls with center x and radius r are written as B(x, r) and B̄(x, r), respectively, and we use the abbreviations ...

A Class of Hereditarily $ell_p(c_0)$ Banach spaces

We extend the class of Banach sequence spaces constructed by Ledari, as presented in ''A class of hereditarily $ell_1$ Banach spaces without Schur property'' and obtain a new class of hereditarily $ell_p(c_0)$ Banach spaces for $1leq p<infty$. Some other properties of this spaces are studied.

On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

A New Class of Banach Sequence Spaces

Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.