On subnormal operators whose spectrum are multiply connected domains.
On the Beurling-Lax theorem for domains with one hole.
On the largest analytic set for cyclic operators.
On the normality of operators.
On the Range and the Kernel of Derivations
2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.Let H be a separable infinite dimensional complex Hilbert space and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A ∈ L(H), the derivation δA : L(H)→ L(H) is defined by δA(X) = AX-XA. In this paper we prove that if A is an n-multicyclic hyponormal operator and T is hyponormal such that AT = TA, then || δA(X)+T|| ≥ ||T|| for all X ∈ L(H). We establish the same inequality if A is...
On the range-kernel orthogonality of elementary operators
Let denote the algebra of operators on a complex infinite dimensional Hilbert space . For , the generalized derivation and the elementary operator are defined by and for all . In this paper, we exhibit pairs of operators such that the range-kernel orthogonality of holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of with respect to the wider class of unitarily invariant norms on...
On the reflexivity of multigenerator algebras [Book]
On the spectra of some non-normal operators.
On the Spherical Spectrum.
On the class operators.
On totally -paranormal operators
In this paper we study some properties of a totally -paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally -paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally -paranormal operators through the local spectral theory. Finally, we show that every totally -paranormal operator satisfies an analogue of the single valued extension property for and some of totally -paranormal operators have scalar extensions....
On two classes of weighted shifts.
On unbounded hyponormal operators III
The paper deals mostly with spectral properties of unbounded hyponormal operators. Some nontrivial examples of such operators are given.
On w-hyponormal operators
We study some properties of w-hyponormal operators. In particular we show that some w-hyponormal operators are subscalar. Also we state some theorems on invariant subspaces of w-hyponormal operators.
Operator equations and subscalarity
We consider the system of operator equations ABA = A² and BAB = B². Let (A,B) be a solution to this system. We give several connections among the operators A, B, AB, and BA. We first prove that A is subscalar of finite order if and only if B is, which is equivalent to the subscalarity of AB or BA with finite order. As a corollary, if A is subscalar and its spectrum has nonempty interior, then B has a nontrivial invariant subspace. We also provide examples of subscalar operator matrices. Moreover,...
Operator norm inequalities of Minkowski type.
Operators of the q-oscillator
We scrutinize the possibility of extending the result of [19] to the case of q-deformed oscillator for q real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whether a solution of the commutation relation is bounded or not. Our leitmotif is subnormality. The deformation parameter q is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator C, has two remarkable properties: it...
Operators with absolute continuity properties: an application to quasinormality
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerge in this context are found. Various examples and counterexamples illustrating the concepts of the paper are constructed by using weighted shifts on directed trees. Generalizations of these results that cover the case of q-quasinormal operators are established.