PROPERTIES OF SLANT TOEPLITZ-OPERATORS

A slant Toeplitz operator A(phi) with symbol phi in L(infinity)(partia l derivative D) is an operator on L(2)(partial derivative D) whose rep resenting matrix M = (alpha(ij)) is given by alpha(ij)= [phi,z(2i-j)] where [.,.] is the usual inner product on L(2)(partial derivative D). Basic properties such as norm, spectrum, compactness and the eigenvect ors of this type of operator are studied. Some algebraic properties ar e also considered. In addition, an interesting decomposition of a mult iplication operator into slant Toeplitz operators is obtained.