Properties of slant Toeplitz operators

A slant Toeplitz operator A(phi) with symbol phi in L(infinity)(partial derivative D) is an operator on L(2)(partial derivative D) whose representing 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 eigenvectors of this type of operator are studied. Some algebraic properties are also considered. In addition, an interesting decomposition of a multiplication operator into slant Toeplitz operators is obtained.