The Toeplitz-Hausdorff and Spectral Inclusion Theorems for Linear Relations
|The Toeplitz-Hausdorff and Spectral Inclusion Theorems for Linear Relations
|Year of Publication
|Kito, SLuliro, Wanjala, G
|International Journal of Mathematics and Computer Science
|June 7, 2021)
|Convexity, Linear relation, Numerical range, Spectral inclusion
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.