On diagonalizable operators in Minkowski spaces with the Lipschitz property
Abstract
A real semiinnerproduct 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 wellknown that the function $x = \sqrt{[x,x]}$ defines a norm on $\M$. and vica versa, for every norm on $X$ there is a semiinnerproduct 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 semiinnerproduct spaces satisfying a certain smoothness condition.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 DOI:
 10.48550/arXiv.1003.2285
 arXiv:
 arXiv:1003.2285
 Bibcode:
 2010arXiv1003.2285L
 Keywords:

 Mathematics  Functional Analysis;
 47A05;
 52A21;
 46B25
 EPrint:
 8 pages, 1 figure