On diagonalizable operators in Minkowski spaces with the Lipschitz property

Details On diagonalizable operators in Minkowski spaces with the Lipschitz property On diagonalizable operators in Minkowski spaces with the Lipschitz property

2010-03-11

arxiv.org/abs/1003.2285v5

Mathematics

Functional Analysis

8 pages, 1 figure

Scientific paper

10.1016/j.laa.2010.07.029

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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