Browsing by Author "Ombaka, C. Ochieng"

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Conjecture of banach space operator ideals in nuclear spaces
(2013-06) Wabomba, Musundi S.; Ombaka, C. Ochieng; Njogu, S. Muriuki; Muthengi, Fredrick; Mugambi, Dennis; Aywa, Shem O.
We apply the notion of Banach space operator ideals in nuclear spaces through topological vector spaces. The motivation for this study came from attempts to generalize the structure of nuclear spaces as a result of nuclear maps from functional analysis context. The compact closed structure associated with the category of relations results to nuclear ideals. Basic properties of Banach space operator ideals in relation to the structure of nuclear spaces will be demonstrated. We therefore establish a close correspondence between Banach space operator ideals and nuclear ideals through topological vector spaces.
On the Banach Space Numerical Range for a Linear Operator ",
(Modern Scientific Press Company, Florida, USA, 2019-03-25) Ohuru, Priscah M.; Musundi, Sammy W. *; Ombaka, C. Ochieng
The numerical range has been studied extensively in Hilbert spaces. Properties of the numerical range such as non-emptiness, containment of the spectrum and in particular, convexity have been proved and results have been given in these spaces. Furthermore, comparison of the numerical ranges with the spectra have been established. In this study, we consider the Banach space numerical range for a linear operator based on the definition by Lumer (1961) and establish its properties in relation to the above stated. Properties of the corresponding Banach numerical radius and spectrum are also discussed. (1) (PDF) On the Banach Space Numerical Range for a Linear Operator. Available from: https://www.researchgate.net/publication/332543193_On_the_Banach_Space_Numerical_Range_for_a_Linear_Operator [accessed Sep 30 2020].