Approximations of Antieigenvalue and Antieigenvalue-Type Quantities
We will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/318214 |
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| author | Morteza Seddighin |
| author_facet | Morteza Seddighin |
| author_sort | Morteza Seddighin |
| collection | DOAJ |
| description | We will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue and Kantorovich inequality. In the second section, we approximate several antieigenvalue-type quantities for arbitrary accretive operators. Each antieigenvalue-type quantity is approximated in terms of the same quantity for normal matrices. In particular, we show that for an arbitrary accretive operator, each antieigenvalue-type quantity is the limit of the same quantity for a sequence of finite-dimensional normal matrices. |
| format | Article |
| id | doaj-art-1e4acf6ea1a147f8b7202dccf0c6b2c2 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1e4acf6ea1a147f8b7202dccf0c6b2c22025-08-20T02:04:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/318214318214Approximations of Antieigenvalue and Antieigenvalue-Type QuantitiesMorteza Seddighin0Mathematics Department, Indiana University East, Richmond, IN 47374, USAWe will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue and Kantorovich inequality. In the second section, we approximate several antieigenvalue-type quantities for arbitrary accretive operators. Each antieigenvalue-type quantity is approximated in terms of the same quantity for normal matrices. In particular, we show that for an arbitrary accretive operator, each antieigenvalue-type quantity is the limit of the same quantity for a sequence of finite-dimensional normal matrices.http://dx.doi.org/10.1155/2012/318214 |
| spellingShingle | Morteza Seddighin Approximations of Antieigenvalue and Antieigenvalue-Type Quantities International Journal of Mathematics and Mathematical Sciences |
| title | Approximations of Antieigenvalue and Antieigenvalue-Type Quantities |
| title_full | Approximations of Antieigenvalue and Antieigenvalue-Type Quantities |
| title_fullStr | Approximations of Antieigenvalue and Antieigenvalue-Type Quantities |
| title_full_unstemmed | Approximations of Antieigenvalue and Antieigenvalue-Type Quantities |
| title_short | Approximations of Antieigenvalue and Antieigenvalue-Type Quantities |
| title_sort | approximations of antieigenvalue and antieigenvalue type quantities |
| url | http://dx.doi.org/10.1155/2012/318214 |
| work_keys_str_mv | AT mortezaseddighin approximationsofantieigenvalueandantieigenvaluetypequantities |