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On the spectrum of positive operators
 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 Gsolvable 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 ALspaces which guanantee that 1 is an eigenvalue. As we know from [17], if T : EE 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 ºorder continuity do not imply ideal irreducibility [2], we prove the analogous results for band irreducible, ºorder 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 Gsolvable 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 ALspaces which guanantee that 1 is an eigenvalue. As we know from [17], if T : EE 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 ºorder continuity do not imply ideal irreducibility [2], we prove the analogous results for band irreducible, ºorder 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 

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