Journal ArticleDOI
The Structure of a Positive Linear Integral Operator
Paul Nelson,Paul Nelson +1 more
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This article is published in Journal of The London Mathematical Society-second Series.The article was published on 1974-10-01. It has received 15 citations till now. The article focuses on the topics: Compact operator & Shift operator.read more
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On the core of a cone-preserving map
Bit Shun Tam,Hans Schneider +1 more
TL;DR: In this paper, the authors studied the Perron-Frobenius theory of nonnegative matrices and its generalizations from the cone-theoretic viewpoint, and showed a one-to-one correspondence between the distinguished /1-invariant faces of a nonnegative matrix and the cycles of the permutation induced by A on the extreme rays of core^f/l, provided that the latter cone is nonzero, simplicial.
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On linear integral operators with nonnegative kernels
TL;DR: In this article, the analysis by Nelson can be enlarged to provide a more complete generalization of the normal form of a nonnegative matrix which can be used to characterize the distinguished eigenvalues of K and K ∗, and to describe sets of support for the eigenfunctions and generalized eigen functions of both K and k ∗ belonging to the spectral radius of K.
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On the ideal structure of positive, eventually compact linear operators on Banach lattices
TL;DR: In this article, the structure of the algebraic eigenspace corresponding to the spectral radius of a nonnegative reducible linear operator T, having a compact iterate and defined on a Banach lattice E with order continuous norm, is studied.
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The structure of the algebraic eigenspace to the spectral radius of eventually compact, nonnegative integral operators
TL;DR: In this paper, the authors extended the analysis of Rothblum [19] to the algebraic eigenspaces of K and K∗ and provided necessary and sufficient conditions in terms of significant k-components for both k and K ∗ to possess a positive eigenfunction corresponding to the spectral radius of K. The analysis is made possible by introducing chains, lengths of chains, height, and depth of a significant k component.
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On the invariant faces associated with a cone-preserving map
Bit-Shun Tam,Hans Schneider +1 more
TL;DR: In this article, the authors generalize some of the known combinatorial spectral results on a nonnegative matrix to results for a cone-preserving map on a polyhedral cone, formulated in terms of its invariant faces.