The class of ω-hyponormal operators is introduced. This class contains allp-hyponormal operators. Certain properties of this class of operators are obtained. Among other things, it is shown that ifT is ω-hyponormal, then its spectral radius and norm are identical, and the nonzero points of its joint point spectrum and point spectrum are identical. Conditions under which a ω-hyponormal operator becomes normal, self-adjoint and unitary are given.
AMS Classification47N20 47A30 47B15
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