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Spectral continuity for operator matrices

Published online by Cambridge University Press:  25 July 2002

Slavisă V. Djordjević  and
Young Min Han
Slavisă V. Djordjević
Affiliation:
University of Niš, Faculty of Philosophy, Department of Mathematics, Ćirila and Metodija 2, 18000 Niš, Yugoslavia e-mail: slavdj@archimed.filfak.ni.ac.yu
Young Min Han
Affiliation:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea e-mail: ymhan@math.skku.ac.kr
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In this paper we prove that if M_C=\pmatrix {A&#TAB;C\cr0&#TAB;B} is a 2\times 2 upper triangular operator matrix on the Hilbert space H\bigoplus K and if \sigma (A)\cap \sigma (B)=\emptyset , then \sigma is continuous at A and B if and only if \sigma is continuous at M_C, for every C\in B(K,H{\hskip1}).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 3 , May 2001 , pp. 487 - 490
Copyright
2001 Glasgow Mathematical Journal Trust