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arXiv · 1003.2285

On diagonalizable operators in Minkowski spaces with the Lipschitz property

Zsolt Langi
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Abstract

A real semi-inner-product space is a real vector space $\M$ equipped with a function $[.,.] : \M \times \M \to \Re$ which is linear in its first variable, strictly positive and satisfies the Schwartz inequality. It is well-known that the function $||x|| = \sqrt{[x,x]}$ defines a norm on $\M$. and vica versa, for every norm on $X$ there is a semi-inner-product satisfying this equality. A linear operator $A$ on $\M$ is called \emph{adjoint abelian with respect to $[.,.]$}, if it satisfies $[Ax,y]=[x,Ay]$ for every $x,y \in \M$. The aim of this paper is to characterize the diagonalizable adjoint abelian operators in finite dimensional real semi-inner-product spaces satisfying a certain smoothness condition.

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Zsolt Langi. 2010-03-11. On diagonalizable operators in Minkowski spaces with the Lipschitz property. https://doi.org/10.1016/j.laa.2010.07.029

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