Structural and Spectral Properties of k-Quasi Class Q(N) and k-Quasi Class Q?(N) Operators

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce two new classes of operators: k-quasi class Q(N) and k-quasi class Q*(N). An operator T is an element of L(H) is of k-quasi class Q(N) for a fixed real number N >= 1 and k a natural number, if T satisfies N parallel to Tk+1x parallel to 2 <= parallel to Tk+2x parallel to 2 + parallel to Tkx parallel to 2 , for all x is an element of H. An operator T is an element of L(H) is of k-quasi class Q*(N) for a fixed real number N >= 1 and k a natural number, if T satisfies N parallel to T*Tkx parallel to 2 <= parallel to Tk+2x parallel to 2 + parallel to Tkx parallel to 2 , for all x is an element of H. We study structural and spectral properties of these classes of operators. Also we compare this new classes of operators with other known classes of operators.