let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define new notion diagonalization for these operators, which call s-diagonalization. give necessary and sufficient conditions bounded operator in order to be s-diagonalizable. These are terms its range operator. also obtain generalized Spectral Theorem normal operators.

In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.