On numerical ranges of convexoid operators

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dc.contributor.author Otieno, J. A.
dc.contributor.author Okelo, Bernad N.
dc.contributor.author Ongat, Naftali O.
dc.date.accessioned 2018-02-26T10:02:09Z
dc.date.available 2018-02-26T10:02:09Z
dc.date.issued 2017-02
dc.identifier.issn 2456-0235
dc.identifier.uri http://www.ijmst.co/
dc.description.abstract Numerical range is useful in studying operators on Hilbert spaces. In particular, the geometrical properties of numerical range often provide useful information about algebraic and analytic properties of an operator. The theory of numerical range played a crucial role in the study of some algebraic structures especially in the non-associative context. The numerical range of an operator depends strongly upon the base field. Motivated by theoretical study and applications, researchers have considered different generalizations of numerical range. Numerical range of an operator may be a point, or a line segment containing none, one or all of its end points. Numerical range of another operator may be an open set, closed set or neither. In this paper, we give results of numerical range of convexoid operators. Let be an infinite dimensional complex Hilbert space and be algebra of all bounded linear operators on . is said to be convexoid if the closure of the numerical range coincides with the convex hull of its spectrum. In this paper, we determine the numerical ranges of convexoid operators. We employ some results for convexoid operators due to Furuta and numerical ranges due to Shapiro, Furuta and Nakamoto, Mecheri and Okelo. Some properties of numerical ranges are also discussed. en_US
dc.language.iso en en_US
dc.publisher G.I publications en_US
dc.subject Numerical range en_US
dc.subject Convexoid operator en_US
dc.subject Numerical radius en_US
dc.subject Spectrum en_US
dc.title On numerical ranges of convexoid operators en_US
dc.type Article en_US

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