NDLI: $${\mathbb{C}}$$-Algèbres Normées Préhilbertiennes Vérifiant $$||a^2|| = ||a||^2$$

Content Provider	Springer Nature Link
Author	Rochdi, A. Moutassim, A. Hilali, M. R.
Copyright Year	2008
Abstract	Dans ce papier nous montrons que si A est une algèbre complexe, normée, préhilbertienne, algébrique, sans diviseurs de zéro et vérifiant $$\|\|a^2\|\| = \|\|a\|\|^2$$ pour tout $$a \in A$$ . Alors A est de dimension finie et isomorphe à $${{\mathbb{C}}}$$ . Ce dernier nous permet de donner des nouveaux résultats plus généraux que ceux du cas absolument valué. De plus nous donnons un exemple d’une C-algèbre normée, Hilbertienne, sans diviseurs de zéro, de dimension infinie et vérifiant $$\|\|a^2\|\| = \|\|a\|\|^2$$ pour tout $$a \in A$$ .In this paper we prove that if A is a complex, normed, pre-Hilbert, algebraic algebra, without divisor of zero and satisfying $$\|\|a^2\|\| = \|\|a\|\|^2$$ for all $$a \in A$$ . Then A is finite dimensional and isomorphic to $${{\mathbb{C}}}$$ . This last allows us to give some new more general results than those of the case absolute valued. Moreover we give an example of a complex, normed, Hilbert, infinite dimensional algebra, without divisor of zero and satisfying $$\|\|a^2\|\| = \|\|a\|\|^2$$ for all $$a \in A$$ .
Ending Page	41
Page Count	9
Starting Page	33
File Format	PDF
ISSN	01887009
e-ISSN	16614909
Journal	Advances in Applied Clifford Algebras
Issue Number	1
Volume Number	20
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2008-10-06
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Algèbre (préhilbertienne, commutative, associative, alternative, flexible, à puissances associatives, algébrique). Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Applications of Mathematics Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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