Sylvester inertia law in commutative Leibniz algebras with logarithms

• Autorzy: Przeworska-Rolewicz D.
• Języki publikacji: EN

Abstrakty

EN

In algebras with logarithms induced by a given right invertible operator D one can define quadratic forms by means of power mappings induced by logarithmic mapping. Main results of this paper will be concerned with the case when an algebra X under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy+yDx for x, y is an element of dom D. If X is an locally m-convex algebra then these forms have the similar properties as quadratic forms in the Euclidian spaces En, including the Sylvester inertia law.

Słowa kluczowe

EN

metric space; convex space; invertible operator; Leibniz condition; logarithmic mapping; canonical mapping; quadratic form; algebraic analysis

PL

przestrzeń metryczna; przestrzeń wypukła; operator odwracalny; warunek Leibniza; odwzorowanie kanoniczne; odwzorowanie logarytmiczne; analiza algebraiczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 3
• Strony: 659--669
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Przeworska-Rolewicz D.

• Institute of Mathematics Polish Academy of Sciences ul. Śniadeckich 8, P.O. Box 21 00-956 Warszawa 10, Poland,

Bibliografia

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