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Linear Transformations on Symmetric Spaces II

Published online by Cambridge University Press:  20 November 2018

Ming–Huat Lim
Ming–Huat Lim*
Affiliation:
Department of Mathematics, University of Malaya, Kuala Lumpur, Malaysia
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Abstract

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Let U be a finite dimensional vector space over an infinite field F. Let U(r) denote the r–th symmetric product space over U. Let T: U(r) → U(s) be a linear transformation which sends nonzero decomposable elements to nonzero decomposable elements. Let dim U ≥ s + 1. Then we obtain the structure of T for the following cases: (I) F is algebraically closed, (II) F is the real field, and (III) T is injective.

Keywords

15A69
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 2 , 01 April 1993 , pp. 357 - 368
Copyright
Copyright © Canadian Mathematical Society 1993

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