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Research Paper | Mathematics | Kenya | Volume 8 Issue 1, January 2019 | Rating: 6.6 / 10

On Essential Numerical Range and Davis-Wielandt Shell of Hilbert Space Operators

D. O. Owego | N. B. Okelo | Omolo Ongati ^[4]

Abstract: Let the numerical range of the operator T be denoted by W (T), the essential numerical range by We (T) and the Davis-Wielandt shell by DW (T). We discuss the equality of the essential numerical range and the numerical range of the operator T in a complex infinite dimensional Hilbert space H. The results obtained are used to study the instance when the essential numerical range can replace the numerical range in the Davis-Wielandt shell.

Keywords: Numerical range, Essential numerical range, Davis-Wielandt shell

Edition: Volume 8 Issue 1, January 2019,

Pages: 836 - 838