Solvability of (λ, μ)-Commuting Operator Equations for Bounded Generalization of Hyponormal Operators

Abstract

Recently, new generalizations have been presented for the hyponormal operators, which are (N, k)-hyponormal operators and (h, M)-hyponormal operators. Some properties of these concepts have also been proved, one of these properties is that the product of two (N, k)-hyponormal operator is also (N, k)- hyponormal operator and the product of two (h, M)-hyponormal operators is (h, M)-hyponormal operator. In our research, we will reprove these properties by using the (λ, μ)-commuting operator equations, in addition to that we will solve the (λ, μ)-commuting operator equations for (N, k)-hyponormal operators and (h, M)-hyponormal operators.