%A SONG Jia-jia, CAO Xiao-hong, DAI Lei
%T The judgement for the small compact perturbation of SVEP for upper triangular operator matrices
%0 Journal Article
%D 2017
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2016.521
%P 61-67
%V 52
%N 4
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_2284.shtml}
%8 2017-04-20
%X When A∈B(H), B∈B(K)are given, we denote by MC an upper triangular operator matrix, acting on the Hilbert space H⊕K, of the form MC=(A C0 B). The properties of the component A,B are discussed in the matrix such that MC satisfies the single-valued extension property of small compact perturbation by defining a kind of new resolvent set. The necessary and sufficient conditions for upper triangular operator matrix which satisfies the single-valued extension property under small compact perturbation are studied, and some examples are given to illustrate the essence of the conditions given in the main theorem.