Rank 1 transformations serve as a source of examples in ergodic theory showing variety algebraic, asymptotic, and spectral properties dynamical systems. The rank one transformation are closely related to the structure semigroup weak limits its powers. In this vein, known new constructions studied.

Quantics tensor train (QTT), a new data-sparse format for one– and multi–dimensional vectors, is based on a bit representation of mode indices followed by a separation of variables. A radix-2 reccurence, that lays behind the famous FFT algorithm, can be efficiently applied to vectors in the QTT format. If input and all intermediate vectors of the FFT algorithm have moderate QTT ranks, the resul...

let a be a bounded linear operator on a banach space x. we investigate the conditions of existing rank-one operator b such that i+f(a)b is invertible for every analytic function f on sigma(a). also we compare the invariant subspaces of f(a)b and b. this work is motivated by an operator method on the banach space ell^2 for solving some pdes which is extended to general operator space under some ...

We prove a spectral perturbation theorem for rank-one updated matrices of special structure. Two applications of the result are given to illustrate the usefulness of the theorem. One is for the spectrum of the Google matrix and the other is for the algebraic simplicity of the maximal eigenvalue of a positive matrix. c © 2007 Elsevier Ltd. All rights reserved.