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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 \(T\).

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