On the Convergence of Orbits in Sequence Space l^2

Abstract

This paper discusses the convergence of orbits for diagonal operators defined on . In particular, the basis elements of  are obtained using the linear combinations of the elements of the orbit. Furthermore, via the classical result of the determinant of the Vandermonde matrix, it is shown that, the more the elements of the orbit are used, the faster the convergence of the orbit to the basis elements of .

Keywords: Diagonal operators; Convergence of Orbits of operators; Vandermonde matrix; Norm topology