The Toeplitz-Hausdorff and Spectral Inclusion Theorems for Linear Relations

TitleThe Toeplitz-Hausdorff and Spectral Inclusion Theorems for Linear Relations
Publication TypeJournal Article
Year of Publication2021
AuthorsKito, SLuliro, Wanjala, G
JournalInternational Journal of Mathematics and Computer Science
Volume16
Issue4
Pagination1637–1645
Date PublishedJune 7, 2021)
KeywordsConvexity, 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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