Spectral continuity for operator matrices
In this paper we prove that if M_C=\pmatrix {A C\cr0 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}).
Saved in:
| Published in | Glasgow mathematical journal Vol. 43; no. 3; pp. 487 - 490 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.05.2001
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | In this paper we prove that if M_C=\pmatrix {A C\cr0 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}). |
|---|---|
| Bibliography: | istex:CDA1F235B50C8DA7C85909B38686BE58DABFEE33 ark:/67375/6GQ-P1T8MN66-T PII:S0017089501030105 |
| ISSN: | 0017-0895 1469-509X |
| DOI: | 10.1017/S0017089501030105 |