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.

## 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 |

### Actions (login required)

View Item |