On class (BD) Operators
Department of Mathematics and computing, Rongo University, Kitere Hills Kenya.
Review Article
World Journal of Advanced Research and Reviews, 2021, 11(02), 048–052
Article DOI: 10.30574/wjarr.2021.11.2.0355
Publication history:
Received on 26 June 2021; revised on 02 August 2021; accepted on 05 August 2021
Abstract:
In this paper, we introduce the class of (BD) operators acting on a complex Hilbert space H. An operator if T ∈ B (H) is said to belong to class (BD) if T * 2 (TD) 2 commutes with (T *TD) 2 equivalently [T * 2 (TD) 2, (T *TD) 2] = 0. We investigate the properties of this class and we also analyze the relation of this class to D-operator and then generalize it to class (nBD) and analyze its relation to the class of n-power D-operator through complex symmetric operators.
Keywords:
D-operator; Normal; N Quasi D-operator; Complex symmetric operators; N-power D-operator; (BD) Operators
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