We characterize the Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains in terms of the Berezin transform.
Let be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with , such as the heat semigroup and Riesz transform, are not, in general, of Calderón-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in , Sobolev, and some new Hardy spaces naturally associated to . First, we show that the...
Let be the symmetric operator given by the restriction of to , where is a self-adjoint operator on the Hilbert space and is a linear dense set which is closed with respect to the graph norm on , the operator domain of . We show that any self-adjoint extension of such that can be additively decomposed by the sum , where both the operators and take values in the strong dual of . The operator is the closed extension of to the whole whereas is explicitly written in terms...
An eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new sufficient conditions for a sequence of infinite order linear differential operators to be hypercyclic on the space of holomorphic functions on certain domains of are shown. Moreover, several necessary conditions are furnished. The equicontinuity of a family of operators as above is also studied, and it is characterized if the domain is . The results obtained extend or improve earlier work...
Simple examples of bounded domains are considered for which the presence of peculiar corners and edges in the boundary causes that the double layer potential operator acting on the space of all continuous functions on can for no value of the parameter be approximated (in the sub-norm) by means of operators of the form (where is the identity operator and is a compact linear operator) with a deviation less then ; on the other hand, such approximability turns out to be possible for...
It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i....
We discuss the problem of characterizing the possible asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces. In particular, given an increasing sequence of positive numbers tending to infinity, we construct Banach spaces such that the norm of the iterates of a suitable multiplication operator between these spaces assumes (or exceeds) the values of this sequence.