tailieunhanh - Báo cáo hóa học: " Research Article Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID61313 8 pages doi 2007 61313 Research Article Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball Ze-Hua Zhou and Cheng Yuan Received 28 February 2007 Accepted 19 October 2007 Recommended by Andras Ronto Let Bn be the unit ball in the N-dimensional complex space for y a holomorphic function in Bn and y a holomorphic map from Bn into itself the weighted composition operator on the weighted Hardy space H2 Bn is given by Cy y f y z f y z where f e H2 fi Bn . This paper discusses the spectrum of Cy y when it is compact on a certain class of weighted Hardy spaces and when the composition map y has only one fixed point inside the unit ball. Copyright 2007 . Zhou and C. Yuan. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction It is well known that the general principle that the spectrum structure of the composition operator Cy is closely related to the fixed point behavior of the map y is well illustrated by compact composition operators. Determining the spectrum of a compact operator is equivalent to finding the eigenvalues of the operator. About the spectrum of a compact operator in a weighted Hardy space defined in the disk or Bn we refer the reader to see 1 where Cowen and MacCluer proved a theorem of considerable generality which will show that essentially all of the spaces of interest to us these eigenvalues are determined by the derivative of y at the Denjoy-Wolff fixed point of y. Weighting a composition operator as a generalization of a multiplication operator and a composition operator recently Gunatillake in 2 obtained some results for the spectrum of weighted composition operators on the weighted Hardy spaces of the unit disk. It is .