TAILIEUCHUNG - Báo cáo toán học: "Some remarks on local spectral theory "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Một số nhận xét về lý thuyết phổ của địa phương. | J. OPERATOR THEORY 12 1984 285-317 Copyright by INCREST 1984 SOME REMARKS ON LOCAL SPECTRAL THEORY E. ALBRECHT and R. D. MEHTA 1. INTRODUCTION There are several possibilities to obtain a local spectral theory for a bounded linear operator T on a complex Banach space X. For example one may consider a suitable unital closed subalgebra 3 of X the algebra of all bounded linear operators on X or of the Calkin algebra Q X X Jf such that T resp. T X X is an element of sd. If sđ is semi-simple then this algebra jaZ can be represented as an algebra of vector valued functions in the sense of G. R. Allan 8 over the compact Hausdorff space Wỉz of all extendable maximal ideals of some unital central subalgebra z of sđ where z is endowed with some norm I z such that Z - z is a Banach algebra. We refer to 8 for more details. This method which gives a local spectral theory for T in the framework of Banach algebra theory has been successfully applied to the study of Toeplitz operators Hankel operators and others see for example 17 18 19 30 31 . Another kind of local spectral theory is obtained if one considers the spectral decomposition properties of T with respect to the underlying Banach space X. We refer to the monographs 14 22 35 for this spatial local spectral theory. Recall 14 3 that an operator T e X is decomposable if and only if for each open covering Uy u2 of the complex plane c there are closed invariant subspaces Fi y2 for 71 with X Yy 4- y2 and such that the spectrum sp T y of TỊ Yj is contained in Uj j 1 2 . This class of operators is rather large. It contains the class of spectra operators in the sense of 22 the class of Riesz operators and more generally the class of -decomposable operators in the sense of I. Colojoara and c. Foia 14 . However there are some important operators of mathematical analysis such as Toeplitz operators with continuous or more general with quasicon-tinuous symbol which are not decomposable in spite of the fact that they have rich functional

• Báo cáo khoa học
• báo cáo của tạp chí Journal of Operator Theory
• tài liệu báo cáo nghiên cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• tài liệu báo cáo nghiện cứu khoa học