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Full Length Research Paper
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Norm properties of operators whose norms are Eigenvalues
A. W. Wafula*,
J. M. Khalagai and G. Pokhariyal
School of
Mathematics, University of Nairobi, P. O. Box 30197, Nairobi,
Kenya.
*Corresponding author
E-mail: arthurwanyonyi@yahoo.com.
Accepted 19 May, 2010 |
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Abstract |
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In this paper we present
properties of a norm-attaining operator on a Hilbert space and
there implications.
We show that if T has norm attaining vector then
where the scalars are nonnegative numbers. Thus T
satisfies a
generalized Daugavet condition.
Key words:
Numerical range, eigenvalue, normalloid operator, Daugavet
property.
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