The ideal structure of the algebraic eigenspace to the spectral radius of eventually compact, reducible, positive linear operators

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The ideal structure of the algebraic eigenspace to the spectral radius of eventually compact, reducible, positive linear operators

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dc.creator Jang, Ruey-jen
dc.date.available 2011-02-18T18:58:19Z
dc.date.issued 1990-08
dc.identifier.uri http://hdl.handle.net/2346/8848 en_US
dc.description.abstract The classical Perron-Frobenius theory, concerning the distribution of Eigen-values of a nonnegative square matrix A, has been applied in recent years to study the positivity structure of the algebraic Eigen-space belonging to the spectral radius of A. The most complete result is by U.G. Rothblum [Linear Algebra and its Applications 12 (1975), 281-292] who showed that the algebraic Eigen-space can be chosen to consist of a basis each with nonnegative components. This result was applied in a clever way to provide necessary and sufficient conditions concerning solvability of nonnegative matrix equations by S. Friedland and H. Schneider and by H.D. Victory, Jr. [SIAM Journal on Algebraic and Discrete Methods 1 (1980), 185-200; respectively, 6 (1985), 406-412]. The work by U. Rothblum was extended to the setting of eventually compact, nonnegative integral operators on Lp-space, p > 1, by H.D. Victory, Jr. [Journal of Mathematical Analysis and Applications 90 (1982), 484-516]. This thesis consists of two results extending the work by H.D. Victory, Jr., cited in the preceding paragraph. The first portion of this thesis provides necessary and sufficient conditions for nonnegative integral operator equations of the form ëf = Kf + g to possess a nonnegative solution f in Lp when ë > 0 and g is a given and nonnegative element in Lp, p > 1. The second portion studies the lattice ideal structure of the algebraic Eigen-space of an eventually compact positive linear operator belonging to its spectral radius.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Texas Tech University en_US
dc.subject Positive operators en_US
dc.subject Eigenvectors en_US
dc.subject Banach lattices en_US
dc.title The ideal structure of the algebraic eigenspace to the spectral radius of eventually compact, reducible, positive linear operators
dc.type Dissertation
thesis.degree.name Ph.D.
thesis.degree.level Doctoral
thesis.degree.discipline Mathematics
thesis.degree.grantor Texas Tech University
thesis.degree.department Mathematics
thesis.degree.department Mathematics and Statistics
dc.degree.department Mathematics en_US
dc.rights.availability Unrestricted.

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