TAILIEUCHUNG - Báo cáo toán học: "Equality of essential spectra of quasisimilar quasinormal operators "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Bình đẳng của quang phổ quan trọng của các nhà khai thác quasisimilar quasinormal. | J. OPERATOR THEORY 3 1980 57-69 g Copyright by INCREST 198Ơ EQUALITY OF ESSENTIAL SPECTRA OF QUASISIMILAR QUASINORMAL OPERATORS L. R. WILLIAMS In this paper all Hilbert spaces are complex. If ye is a Hilbert space we denote by the algebra of all bounded linear operators on ye. In this paper we shall use the term operator to mean an element of ye for some Hilbert space ye. An operator T is said to be quasinormal if T commutes with T T. If T is an operator and TT T T then T is said to be hyponormal. It is known that every quasinormal operator is hyponormal cf. 1 5 . If ye and ye are Hilbert spaces and X-. ye - is a bounded linear transformation having trivial kernel and dense range then X is called a quasiaffinity. If Tr e SeXY and u e y and there exist quasiaffinities X ye ye and Y ye ye satisfyingXTx Tffiand TXY YT2 then Tx and T2 are said to be quasisimilar. If T is an operator let a T denote the spectrum of T. If T e ye and ye is an infinite dimensional Hilbert space let T denote the image of T in the Calkin algebra ye j under the natural quotient map and let affiT denote the essential spectrum of T . the spectrum of T S denotes the norm-closed ideal of all compact operators in S. y Ỵ . Let Tx and T2 be quasisimilar hyponormal operators on infinite dimensional Hilbert spaces s. Clary proved in 3 that j T ơ T2 . The present author showed in 9 that there are several cases which imply re Ti ơeíTa . For example if Tx and T2 are both biquasitriangular if T and T2 are both weighted shifts bilateral or unilateral or if Tx and T2 are both partial isometries then ơe Fi ơeỢ 2 . The purpose of this paper is to prove that if Tj and T2 are both quasinormal then ơe Ti ơeíU . Suppose that T is an operator. Then T is unitarily equivalent to Tf T2 where Tx is normal and Ta is pure or completely non-normal . if .z - is a reducing subspace of T2 and T21Jf is normal then Jf 0 . The operator Tx is called the normal part of T and T2 the pure part of T. Note that either of the .

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