PROPERTIES OF RATIONALIZED TOEPLITZ HANKEL OPERATORS

In this paper, we introduce and study the notion of Rationalized Toeplitz Hankel Matrix of order (k1, k2) as the two way infinite matrix (alpha ij) such that alpha ij = alpha i+k2,j+k1where k1 and k2 are relatively prime non zero integers. It is proved that a bounded linear operator R on L2 is a Rationalized Toeplitz Hankel operator [5] of order (k1, k2) if and only if its matrix w.r.t. the orthonormal basis {zi : i is an element of Z} is a Rationalized Toeplitz Hankel matrix of the same order. Some algebraic properties of the Rationalized Toeplitz Hankel operator R phi like normality, hyponormality and compactness are also discussed.