On the Spectra of Some Non-Normal Operators

In this paper, we prove the following: (1) If T is invertible w-hyponormal completely non-normal, then the point spectrum is empty. (2) If T1 and T2 are injective !-hyponormal and if T and S are quasisimilar, then they have the same spectra and essential spectra. (3) If T is (p, k)-quasihyponormal operator, then σjp(T)−{0} = σap(T)−{0}. (4) If T*, S 2 element of (H) are injective (p, k)-quasihyponormal operator, and if XT = SX, where X element of B(H) is an invertible, then there exists a unitary operator U such that UT = SU and hence T and S are normal operators.