On numerical range and spectrum of linear operators on G.S.I.P.\ spaces

Huche Gowda, and Lokesha, V. (2001) On numerical range and spectrum of linear operators on G.S.I.P.\ spaces. J. Natur. Phys. Sci., 15 (1-2). pp. 25-30.

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Abstract

Review : A generalized semi-inner product space is a complex linear space X equipped with a generalized semi-inner product (g.s.i.p.), [⋅,⋅]:X×X→C, satisfying the following conditions: [αx+βy,z]=α[x,z]+β[y,z], [x,x]>0 for x≠0, |[x,y]|≤[x,x]1p[y,y]p−1p (here the notation in the paper is misleading), 1<p<∞, for all x,y,z∈X and for all α,β∈C. The authors assert that a g.s.i.p. is a normed linear space whose norm is given by ∥x∥=[x,x]1p. It is not clear to the reviewer how the property ∥αx∥=|α|∥x∥ can be established from the above axioms. They define the numerical range Wp(T) on a g.s.i.p. and generalize some results on the convexity of numerical ranges and the spectrum of an operator.

Item Type: Article
Subjects: Physical Sciences > Mathematics
Divisions: PG Campuses > Manasagangotri, Mysore > Mathematics
Depositing User: Kodandarama
Date Deposited: 28 May 2013 07:28
Last Modified: 26 Aug 2013 11:26
URI: http://eprints.uni-mysore.ac.in/id/eprint/11466

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