We prove an n-tuple analogue of the Putnam area inequality for the spectrum of a single p-hyponormal operator. Let B…H† denote the algebra of operators (i.e. bounded linear transformations) on a separable Hilbert space H. The operator A 2 B…H† is said to be p-hyponormal, 0 < p 1, if jA j2p jAj2p. Let H…p† denote the class of p-hyponormal operators. Then H…1† consists of the class of p-hyponorma...

Firstly, we will show the following extension of the results on powers of p-hyponormal and log-hyponormal operators: let n andm be positive integers, if T is p-hyponormal for p ∈ (0,2], then: (i) in case m ≥ p, (Tn+mTn+m)(n+p)/(n+m) ≥ (TnTn)(n+p)/n and (TnTn ∗ )(n+p)/n ≥ (Tn+mTn+m)(n+p)/(n+m) hold, (ii) in case m < p, Tn+mTn+m ≥ (Tn ∗ Tn)(n+m)/n and (TnTn ∗ )(n+m)/n ≥ Tn+mTn+m hold. Secondly, w...

In this paper, we give an extension of the orthogonality results to dominant operators and p-hyponormal or log-hyponormal operators, also we will generalize some commutativity results. AMS 2000 Mathematics Subject Classification. 47B47, 47A30, 47B20.

In 1984 M. Putinar proved that hyponormal operators are subscalar operators of order two. The proof provided a concrete structure of such operators. We will use this structure to give a sufficient condition for hyponormal operators T with trace-class commutator to admit a direct summand S so that T ⊕ S is the sum of a normal operator and a HilbertSchmidt operator. We investigate what this suffi...

Let A be a bounded linear operator acting on infinite dimensional separable Hilbert space H. Browder’s theorem and a-Browder’s theorem are related to an important property which has a leading role on local spectral theory: the single valued extension property see the recent monograph by Laursen and Neumann [19]. The study of operators satisfying Browder’s theorem is of significant interest, and...

Toeplitz operators (or equivalently, Wiener-Hopf operators; more generally, block Toeplitz operators; and particularly, Toeplitz determinants) are of importance in connection with a variety of problems in physics, and in particular, in the field of quantum mechanics. For example, a study of solvable models in quantum mechanics uses the spectral theory of Toeplitz operators (cf. [Pr]); the one-d...