Numerical Range of Two Operators in Semi-Inner Product Spaces
In this paper, the numerical range for two operators (both linear and nonlinear) have been studied in semi-inner product spaces. The inclusion relations between numerical range, approximate point spectrum, compression spectrum, eigenspectrum, and spectrum have been established for two linear operato...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/846396 |
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| _version_ | 1832555893798993920 |
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| author | N. K. Sahu C. Nahak S. Nanda |
| author_facet | N. K. Sahu C. Nahak S. Nanda |
| author_sort | N. K. Sahu |
| collection | DOAJ |
| description | In this paper, the numerical range for two operators (both linear and nonlinear) have
been studied in semi-inner product spaces. The inclusion relations between numerical
range, approximate point spectrum, compression spectrum, eigenspectrum, and spectrum
have been established for two linear operators. We also show the inclusion relation between
approximate point spectrum and closure of the numerical range for two nonlinear
operators. An approximation method for solving the operator equation involving two
nonlinear operators is also established. |
| format | Article |
| id | doaj-art-f1318dab02ae495a94c8b2a21bafb5cf |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f1318dab02ae495a94c8b2a21bafb5cf2025-02-03T05:47:01ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/846396846396Numerical Range of Two Operators in Semi-Inner Product SpacesN. K. Sahu0C. Nahak1S. Nanda2Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, IndiaDepartment of Mathematics, Indian Institute of Technology, Kharagpur 721302, IndiaKIIT University, Bhubaneswar 751024, IndiaIn this paper, the numerical range for two operators (both linear and nonlinear) have been studied in semi-inner product spaces. The inclusion relations between numerical range, approximate point spectrum, compression spectrum, eigenspectrum, and spectrum have been established for two linear operators. We also show the inclusion relation between approximate point spectrum and closure of the numerical range for two nonlinear operators. An approximation method for solving the operator equation involving two nonlinear operators is also established.http://dx.doi.org/10.1155/2012/846396 |
| spellingShingle | N. K. Sahu C. Nahak S. Nanda Numerical Range of Two Operators in Semi-Inner Product Spaces Abstract and Applied Analysis |
| title | Numerical Range of Two Operators in Semi-Inner
Product Spaces |
| title_full | Numerical Range of Two Operators in Semi-Inner
Product Spaces |
| title_fullStr | Numerical Range of Two Operators in Semi-Inner
Product Spaces |
| title_full_unstemmed | Numerical Range of Two Operators in Semi-Inner
Product Spaces |
| title_short | Numerical Range of Two Operators in Semi-Inner
Product Spaces |
| title_sort | numerical range of two operators in semi inner product spaces |
| url | http://dx.doi.org/10.1155/2012/846396 |
| work_keys_str_mv | AT nksahu numericalrangeoftwooperatorsinsemiinnerproductspaces AT cnahak numericalrangeoftwooperatorsinsemiinnerproductspaces AT snanda numericalrangeoftwooperatorsinsemiinnerproductspaces |