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On the spectrum of positive operators

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Date Issued:
2012
Summary:
Spectral theory, mathematical system theory, evolution equations, differential and difference equations [electronic resource] : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010.It is known that lattice homomorphisms and G-solvable positive operators on Banach lattices have cyclic peripheral spectrum (See [17]). In my thesis I prove that positive contractions whose spectral radius is 1 on Banach lattices with increasing norm have cyclic peripheral point spectrum. I also prove that if the Banach lattice is a K B space satisfying the growth conditon and º is an eigenvalue of a positive contraction T such that [º] = 1, then 1 is also an eigenvalue of T as well as an eigenvalue of T¨, the dual of T. I also investigate the conditions on contraction operators on Hilbert lattices and AL-spaces which guanantee that 1 is an eigenvalue. As we know from [17], if T : E-E is a positive ideal irreducible operator on E such the r (T) = 1 is a pole of the resolvent R(º, T), then r (T) is simple pole with dimN (T -r(T)I) and ºper(T) is cyclic. Also all points of ºper(T) are simple poles of the resolvent R(º,T). SInce band irreducibility and º-order continuity do not imply ideal irreducibility [2], we prove the analogous results for band irreducible, º-order continuous operators.
Title: On the spectrum of positive operators.
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Name(s): Acharya, Cheban P.
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 2012
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: vi, 53 p. : ill.
Language(s): English
Summary: Spectral theory, mathematical system theory, evolution equations, differential and difference equations [electronic resource] : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010.It is known that lattice homomorphisms and G-solvable positive operators on Banach lattices have cyclic peripheral spectrum (See [17]). In my thesis I prove that positive contractions whose spectral radius is 1 on Banach lattices with increasing norm have cyclic peripheral point spectrum. I also prove that if the Banach lattice is a K B space satisfying the growth conditon and º is an eigenvalue of a positive contraction T such that [º] = 1, then 1 is also an eigenvalue of T as well as an eigenvalue of T¨, the dual of T. I also investigate the conditions on contraction operators on Hilbert lattices and AL-spaces which guanantee that 1 is an eigenvalue. As we know from [17], if T : E-E is a positive ideal irreducible operator on E such the r (T) = 1 is a pole of the resolvent R(º, T), then r (T) is simple pole with dimN (T -r(T)I) and ºper(T) is cyclic. Also all points of ºper(T) are simple poles of the resolvent R(º,T). SInce band irreducibility and º-order continuity do not imply ideal irreducibility [2], we prove the analogous results for band irreducible, º-order continuous operators.
Identifier: 837323109 (oclc), 3359288 (digitool), FADT3359288 (IID), fau:4068 (fedora)
Note(s): by Cheban P. Acharya.
Thesis (Ph.D.)--Florida Atlantic University, 2012.
Includes bibliography.
Mode of access: World Wide Web.
System requirements: Adobe Reader.
Subject(s): Operator theory
Evolution equations
Banach spaces
Linear topological spaces
Functional analysis
Held by: FBoU FAUER
Persistent Link to This Record: http://purl.flvc.org/FAU/3359288
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU