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POLYNOMIAL AND POLYGONAL CONNECTIONS BETWEEN IDEMPOTENTS IN FINITE-DIMENSIONAL REAL ALGEBRAS

Published online by Cambridge University Press:  28 April 2004

J. ESTERLE  and
J. GIOL
J. ESTERLE
Affiliation:
Laboratoire Bordelais d'Analyse et Géométrie, Université Bordeaux I, 351, cours de la Libération, 33405 Talence, [email protected]
J. GIOL
Affiliation:
Laboratoire Bordelais d'Analyse et Géométrie, Université Bordeaux I, 351, cours de la Libération, 33405 Talence, [email protected]
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Abstract

Let $\idemp$ be the set of idempotents in a finite-dimensional real algebra $A$. Let $p$ and $q$ be idempotents that lie in the same component of $\idemp$. Then, among the continuous paths connecting $p$ and $q$ in $\idemp$, there exist a polynomial path of degree at most $3$ and a polygonal path consisting of at most three segments.

Keywords

46H1016P10
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 3 , May 2004 , pp. 378 - 382
Copyright
© The London Mathematical Society 2004

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Footnotes

This work is part of the research project of the network ‘Analysis and Operators’, Contract HPRN-CT-2000-00116, supported by the European Commission.