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

Abstract

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 ∈ 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 ∥T^k+1(x)∥^2 ≤ ∥T^k+2(x)∥^2 + ∥T^k(x)∥^2, for all x ∈ H.

An operator T ∈ 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 ∥T*T^k(x)∥^2 ≤ ∥T^k+2(x)∥^2 + ∥T^k(x)∥^2, for all x ∈ 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