We study the spectral pictures of (jointly) hyponormal 2-variable weighted shifts with commuting subnormal components. By contrast with all known results in the theory of subnormal single and 2-variable weighted shifts, we show that the Taylor essential spectrum can be disconnected. We do this by obtaining a simple sufficient condition that guarantees disconnectedness, based on the norms of the...

We define the class of almost semi-hyponormal operators on a Hilbert space and provide some sufficient conditions in which such operators are almost normal, that is their self-commutator is in the trace-class. Mathematics Subject Classification: 47B20

We introduce the notion of weak subnormality, which generalizes subnormality in the sense that for the extension b T ∈ L(K) of T ∈ L(H) we only require that b T ∗ b Tf = b T b T ∗f hold for f ∈ H; in this case we call b T a partially normal extension of T . After establishing some basic results about weak subnormality (including those dealing with the notion of minimal partially normal extensio...

Associated with T = U|T | (polar decomposition) in L(H) is a related operator T̃ = |T | 1 2U|T | 1 2 , called the Aluthge transform of T . In this paper we study some connections betweenT and T̃ , including the following relations; the single valued extension property, an analogue of the single valued extension property onWm(D,H), Dunford’s property (C) and the property (β). 2000 Mathematics Subj...

In this paper we study some properties of the sums two composition operators on Hardy space. particular, investigate hyponormality operators. We also provide conditions for which with linear fractional symbols are hyponormal.

Index theory has had profound impact on many branches of mathematics. In this note we discuss the context for a new kind of index theorem. We begin, however, with some operator-theoretic results. In [11] Berger and Shaw established that finitely cyclic hyponormal operators have trace-class self-commutators. In [9], [31] Berger and Voiculescu extended this result to operators whose self-commutat...

We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment pr...

In this paper, we characterize the hyponormal dual Toeplitz operators with special symbols on orthogonal complement of pluriharmonic Bergman space unit ball. Also completely for (semi)commuting operators.