On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences
The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the operator defined by the lambda matrix over the sequence spaces and c. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/687393 |
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| _version_ | 1832561151946260480 |
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| author | Medine Yeşilkayagil Feyzi Başar |
| author_facet | Medine Yeşilkayagil Feyzi Başar |
| author_sort | Medine Yeşilkayagil |
| collection | DOAJ |
| description | The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's
classification of the operator defined by the lambda matrix over the sequence spaces and c. As a new
development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix
operator on the sequence spaces and c. Finally, we present a Mercerian theorem. Since the matrix is
reduced to a regular matrix depending on the choice of the sequence having certain properties and its
spectrum is firstly investigated, our work is new and the results are comprehensive. |
| format | Article |
| id | doaj-art-73ad1c309e404fc9ae9ee128befd4436 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-73ad1c309e404fc9ae9ee128befd44362025-02-03T01:25:52ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/687393687393On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent SequencesMedine Yeşilkayagil0Feyzi Başar1Department of Mathematics, Uşak University, 1 Eylül Campus, 64200 Uşak, TurkeyDepartment of Mathematics, Fatih University, The Hadimköy Campus, Büyükçekmece, 34500 İstanbul, TurkeyThe main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the operator defined by the lambda matrix over the sequence spaces and c. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator on the sequence spaces and c. Finally, we present a Mercerian theorem. Since the matrix is reduced to a regular matrix depending on the choice of the sequence having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.http://dx.doi.org/10.1155/2013/687393 |
| spellingShingle | Medine Yeşilkayagil Feyzi Başar On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences Abstract and Applied Analysis |
| title | On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences |
| title_full | On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences |
| title_fullStr | On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences |
| title_full_unstemmed | On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences |
| title_short | On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences |
| title_sort | on the fine spectrum of the operator defined by the lambda matrix over the spaces of null and convergent sequences |
| url | http://dx.doi.org/10.1155/2013/687393 |
| work_keys_str_mv | AT medineyesilkayagil onthefinespectrumoftheoperatordefinedbythelambdamatrixoverthespacesofnullandconvergentsequences AT feyzibasar onthefinespectrumoftheoperatordefinedbythelambdamatrixoverthespacesofnullandconvergentsequences |