The Toeplitz-Hausdorff and Spectral Inclusion Theorems for Linear Relations
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| Title | The Toeplitz-Hausdorff and Spectral Inclusion Theorems for Linear Relations |
| Publication Type | Journal Article |
| Year of Publication | 2021 |
| Authors | Kito, SLuliro, Wanjala, G |
| Journal | International Journal of Mathematics and Computer Science |
| Volume | 16 |
| Issue | 4 |
| Pagination | 1637–1645 |
| Date Published | June 7, 2021) |
| Keywords | Convexity, Linear relation, Numerical range, Spectral inclusion |
| Abstract | The Toeplitz-Hausdorff Theorem which was established in 1918 asserts that the numerical range of an operator is always convex. We prove this theorem for the numerical range of a linear relation relative to another linear relation. We also show that the closure of this numerical range contains the relative spectrum for these two linear relations. The classical results for a single linear relation can be deduced from the results obtained here. |
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