Properties of absolute-*-k-paranormal operators and contractions for *-A(k) operators

Abstract

First, we see if T is absolute- * -k-paranormal for k ≥ 1, then T is a normaloid operator. We also see some properties of absolute- * -k-paranormal operator and * -A(k) operator. Then, we will prove the spectrum continuity of the class * -A(k) operator for k > 0. Moreover, it is proved that if T is a contraction of the class * -A(k) for k > 0, then either T has a nontrivial invariant subspace or T is a proper contraction, and the nonnegative operatoris a strongly stable contraction. Finally if T ∈ * -A(k) is a contraction for k > 0, then T is the direct sum of a unitary and C·0 (c.n.u) contraction.Mathematics Subject Classification (2010): 47A10, 47B37, 15A18.