The Toeplitz-Hausdorff and Spectral Inclusion Theorems for Linear Relations

Silas Luliro Kito*, Gerald Wanjala

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةمراجعة النظراء

ملخص

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.

اللغة الأصليةEnglish
الصفحات (من إلى)1637-1645
عدد الصفحات9
دوريةInternational Journal of Mathematics and Computer Science
مستوى الصوت16
رقم الإصدار4
حالة النشرPublished - 2021
منشور خارجيًانعم

ASJC Scopus subject areas

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