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International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
www.ijsr.net | Open Access | Fully Refereed | Peer Reviewed International Journal

ISSN: 2319-7064



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

D. O. Owego, N. B. Okelo, Omolo Ongati

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



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