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Positive definite diagonal sequences. (English) Zbl 0867.46017
Let $$E$$ be a complex Banach lattice. The sequence $$(x_n)_{n\in\mathbb{Z}}$$ is called positive definite if for all finite sequences $$(\lambda_n)$$ of complex numbers we have $$\sum_\ell \sum_m\lambda_\ell\overline\lambda_m x_{\ell-m}\geq 0$$. Given the space $$L^r(E)$$ of regular operators on a Dedekind complete Banach lattice $$E$$, consider the projection of a member $$T$$ of $$L^r(E)$$ to the disjoint complement of the center of $$E$$, which is the diagonal of $$T$$. The authors study some properties of positive definite sequences of the diagonals of powers of $$T$$.

##### MSC:
 46B42 Banach lattices 47B65 Positive linear operators and order-bounded operators
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