Properties of absolute-∗-k-paranormal operators and contractions for ∗-A(k) operators - HOXHA, Ilmi; BRAHA, Naim L.; TATO, Agron (Studia Universitatis Babeș-Bolyai Mathematica, 2019)
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 operator 1 D = T ∗|T |2k T k+1 − |T ∗|2 is 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.