tailieunhanh - Báo cáo toán học: "On the spectrum of the hyponormal or semi-hyponormal operators "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Trên quang phổ của các nhà khai thác hyponormal hoặc bán hyponormal. | i 5 Copyright by INCREST 1981 J. OPERATOR THEORY 5 1981 267-282 COMPARING FUNCTORS CLASSIFYING EXTENSIONS OF C -ALGEBRAS JONATHAN ROSENBERG and CLAUDE SCHOCHET 1. INTRODUCTION AND STATEMENT OE RESULTS Suppose that A and B are separable c -algebras. We are concerned with the classification of extensions of c -algebras of the form 0- B X- E- H- 0 where X X X is the c -algebra of compact operators on a complex separable infinite-dimensional Hilbert space w. Of special interest is the case where B C Y the continuous functions vanishing at infinity on a second countable locally compact space Y. When B c the complex numbers equivalently Y pt the one-point space then reduces to 0 - X - E- A - 0. Essential extensions of the form modulo a suitable equivalence relation form a group Ext X provided that A is nuclear by results of Brown Douglas and Fillmore 6 abbreviated hereafter BDF Choi-Effros 8 Voiculescu 21 and Arveson 2 This group has been calculated in terms of topological K-theory when A is commutative by Kahn Kaminker and Schochet 13 generalizing results of BDF. When Bis non-trivial there is a great variety of complicated classification problems associated with extensions see 7 9 and 10 for an idea of the complexity of the subject . Nevertheless there are two approaches which we now describe which identify extensions with elements of commutative semigroups or groups having nice ftinctorial properties. Both approaches begin with the observation of Busby 7 Theorem that every diagram defines canonically a commutative diagram 0 .-- B X -------E A---------------0 I 0----- B X - y B Q B --------------- 0 268 JONATHAN ROSENBERG and CLAUDE SCHOCHET where ưử B denotes the algebra M B X uY of two-sided multipliers of B A B Jl B ị B Jf and the map Tt is the pull-back of T and the quotient map n. When B C0 Y we write Jl Y and Q y for . B and Q B by 1 Theorem and its Corollaries y y maybe identified with csk .y tB the algebra of norm-bounded