Decomposability of nonnegative r-potent operators on L2(X)

We investigate the decomposability of nonnegative compact r-potent operators on a separable Hilbert space L2(X). We provide a constructive algorithm to prove that basis functions of range spaces of nonnegative r-potent operators can be chosen to be all nonnegative and mutually orthogonal. We use thi...

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Bibliographic Details
Published inarXiv.org
Main Authors Rashmi Sehgal Thukral, Marwaha, Alka
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.04.2015
Subjects
Algorithms
Basis functions
Decomposition
Hilbert space
Operators
Orthogonality
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Summary:We investigate the decomposability of nonnegative compact r-potent operators on a separable Hilbert space L2(X). We provide a constructive algorithm to prove that basis functions of range spaces of nonnegative r-potent operators can be chosen to be all nonnegative and mutually orthogonal. We use this orthogonality to establish that nonnegative compact r-potent operators with range spaces of dimension strictly greater than r-1 are decomposable.
ISSN:2331-8422