We study a new class of bounded linear operators which strictly contains the class of bounded linear operators with the decomposition property (δ) or the weak spectral decomposition property (weak-SDP). We treat general local spectral properties for operators in this class and compare them with the case of operators with (δ).
We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.
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....
We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes.
The paper deals mostly with spectral properties of unbounded hyponormal operators. Some nontrivial examples of such operators are given.
We show that a stochastic operator acting on the Banach lattice of all -integrable functions on is quasi-compact if and only if it is uniformly smoothing (see the definition below).
Let be an analytic self-mapping of and an analytic function on . In this paper we characterize the bounded and compact Volterra composition operators from the Bergman-type space to the Bloch-type space. We also obtain an asymptotical expression of the essential norm of these operators in terms of the symbols and .
This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic, (ii) diagonalizable operators are not weakly -sequentially supercyclic, and (iii) weak -sequential supercyclicity is preserved between a unitary operator and its adjoint. On the other hand, weak supercyclicity is investigated for classes of normed-space operators:...