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A simultaneous lifting theorem for block diagonal operators
| Content Provider | Semantic Scholar |
|---|---|
| Author | Allen, George D. Ward, Joseph D. |
| Copyright Year | 1979 |
| Abstract | ABsTRAcr. Stampfli has shown that for a given T E B(H) there exists a K E C(H) so that a(T + K) = a,(T). An analogous result holds for the essential numerical range W,(T). A compact operator K is said to preserve the Weyl spectrum and essential numerical range of an operator T E B(H) if a(T + K) = aG(T) and W(T + K)= W,(T). THEoREm. For each block diagonal operator T, there exists a conmact operator K which presenres the Weyl spectrum and essential numerical range of T. The perturbed operator T + K is not, in general, block diagonal. An example is given of a block diagonal operator T for which there can be no block diagonal perturbation which preserves the Weyl spectrum and essential numerical range of T. |
| Starting Page | 385 |
| Ending Page | 397 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9947-1979-0530063-8 |
| Volume Number | 250 |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1979-250-00/S0002-9947-1979-0530063-8/S0002-9947-1979-0530063-8.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
