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 satisfiesN ∥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
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