Erratum : “Some classical function theory theorems and their modern versions”
The original version of the article was published in Central European Journal of Mathematics, 2005, 3(4), 591–605. Unfortunately, the original version of this article contains a mistake. We give some corrections to our work.
Due to a technical error, part of a sentence was omitted on the top of page 8. The first line should read: “where , or , means the number of folds of the covering ending at p, i.e. covering a neighbourhood of p in without covering p itself”.
In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space.
Let and be holomorphic self-maps of the unit disk, and denote by , the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.
In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator , when is a linear-fractional self-map of . In this paper first, we investigate the essential normality problem for the operator on the Hardy space , where is a bounded measurable function on which is continuous at each point of , , and is the Toeplitz operator with symbol . Then we use these results and characterize the essentially normal...
We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces and for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.
We estimate the essential norm of a weighted composition operator relative to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.
In this paperwe study both the spectra and the essential spectra ofweighted composition operators on Hardy spaces Hp(ⅅ), standard weighted Bergman spaces Apα(ⅅ) and weighted H∞1-type spaces when the symbols are of hyperbolic type