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 complex Hilbert space H. In this paper we introduce two new classes of operators: k−quasi class Q(N ) and Q*(N ). An ∈ L(H) is for fixed real number N ≥ 1 k natural number, if satisfies ∥T^k+1(x)∥^2 ≤ ∥T^k+2(x)∥^2 + ∥T^k(x)∥^2, all x satisfiesN ∥T*T^k(x)∥^2 We study structural spectral properties these operators. Also compare operators with other known