Structure of the antieigenvectors of a strictly accretive operator
A necessary and sufficient condition that a vector f is an antieigenvector of a strictly accretive operator A is obtained. The structure of antieigenvectors of selfadjoint and certain class of normal operators is also found in terms of eigenvectors. The Kantorovich inequality for selfadjoint operat...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298001069 |
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| _version_ | 1832558712761352192 |
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| author | K. C. Das M. Das Gupta K. Paul |
| author_facet | K. C. Das M. Das Gupta K. Paul |
| author_sort | K. C. Das |
| collection | DOAJ |
| description | A necessary and sufficient condition that a vector
f is an antieigenvector of a
strictly accretive operator A is obtained. The structure of antieigenvectors of selfadjoint and certain
class of normal operators is also found in terms of eigenvectors. The Kantorovich inequality for
selfadjoint operators and the Davis's inequality for normal operators are then easily deduced. A
sort of uniqueness is also established for the values of
Re(Af,f) and ‖Af‖ if the first antieigenvalue, which is equal to min Re(Af,f)/(‖Af‖‖f‖) is attained at the unit vector f. |
| format | Article |
| id | doaj-art-35969908d86a4f6fad0c433c0769d718 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-35969908d86a4f6fad0c433c0769d7182025-02-03T01:31:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121476176610.1155/S0161171298001069Structure of the antieigenvectors of a strictly accretive operatorK. C. Das0M. Das Gupta1K. Paul2Department of Mathematics, Jadavpur University, Calcutta 700 032, IndiaDepartment of Mathematics, Jadavpur University, Calcutta 700 032, IndiaDepartment of Mathematics, Jadavpur University, Calcutta 700 032, IndiaA necessary and sufficient condition that a vector f is an antieigenvector of a strictly accretive operator A is obtained. The structure of antieigenvectors of selfadjoint and certain class of normal operators is also found in terms of eigenvectors. The Kantorovich inequality for selfadjoint operators and the Davis's inequality for normal operators are then easily deduced. A sort of uniqueness is also established for the values of Re(Af,f) and ‖Af‖ if the first antieigenvalue, which is equal to min Re(Af,f)/(‖Af‖‖f‖) is attained at the unit vector f.http://dx.doi.org/10.1155/S0161171298001069AntieigenvectorsAccretive Operator. |
| spellingShingle | K. C. Das M. Das Gupta K. Paul Structure of the antieigenvectors of a strictly accretive operator International Journal of Mathematics and Mathematical Sciences Antieigenvectors Accretive Operator. |
| title | Structure of the antieigenvectors of a strictly accretive operator |
| title_full | Structure of the antieigenvectors of a strictly accretive operator |
| title_fullStr | Structure of the antieigenvectors of a strictly accretive operator |
| title_full_unstemmed | Structure of the antieigenvectors of a strictly accretive operator |
| title_short | Structure of the antieigenvectors of a strictly accretive operator |
| title_sort | structure of the antieigenvectors of a strictly accretive operator |
| topic | Antieigenvectors Accretive Operator. |
| url | http://dx.doi.org/10.1155/S0161171298001069 |
| work_keys_str_mv | AT kcdas structureoftheantieigenvectorsofastrictlyaccretiveoperator AT mdasgupta structureoftheantieigenvectorsofastrictlyaccretiveoperator AT kpaul structureoftheantieigenvectorsofastrictlyaccretiveoperator |