The notion of supraposinormality was introduced by Rhaly in a superclass of posinormal operators. In this paper, we give an extension of this notion of supraposinormality to α-supraposinormality of operators in the dense norm-attainable class.

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General characterization of Hilbert space operators has been a subject of interest to many mathematicians for decades. In this paper, we characterize absolute norm-attainability for compact hyponormal operators. We give necessary and sufficient conditions for a bounded linear compact hyponormal operator on an infinite dimensional complex Hilbert space to be absolutely norm attaining. Moreover, we discuss the structure of compact hyponormal operators when they are self-adjoint and normal. Lastly, we discuss in general, other properties of compact hyponormal operators when they are absolutely norm attaining and their commutators.