Characterizations of compact operators on ℓp−type fractional sets of sequences
Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp−type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of...
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| Language: | English |
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De Gruyter
2019-03-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2019-0015 |
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doaj-2d2b40159eb8411fa98b7d409d2298862021-07-01T05:21:52ZengDe GruyterDemonstratio Mathematica2391-46612019-03-0152110511510.1515/dema-2019-0015dema-2019-0015Characterizations of compact operators on ℓp−type fractional sets of sequencesÖzger Faruk0Department of Engineering Sciences, İzmir Katip Çelebi University, 35620,Izmir, TurkeyAmong the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp−type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.https://doi.org/10.1515/dema-2019-0015gamma functionfractional operatoroperator normcompact operatorhausdorff measure of noncompactness46b4547b37 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Özger Faruk |
| spellingShingle |
Özger Faruk Characterizations of compact operators on ℓp−type fractional sets of sequences Demonstratio Mathematica gamma function fractional operator operator norm compact operator hausdorff measure of noncompactness 46b45 47b37 |
| author_facet |
Özger Faruk |
| author_sort |
Özger Faruk |
| title |
Characterizations of compact operators on ℓp−type fractional sets of sequences |
| title_short |
Characterizations of compact operators on ℓp−type fractional sets of sequences |
| title_full |
Characterizations of compact operators on ℓp−type fractional sets of sequences |
| title_fullStr |
Characterizations of compact operators on ℓp−type fractional sets of sequences |
| title_full_unstemmed |
Characterizations of compact operators on ℓp−type fractional sets of sequences |
| title_sort |
characterizations of compact operators on ℓp−type fractional sets of sequences |
| publisher |
De Gruyter |
| series |
Demonstratio Mathematica |
| issn |
2391-4661 |
| publishDate |
2019-03-01 |
| description |
Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp−type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences. |
| topic |
gamma function fractional operator operator norm compact operator hausdorff measure of noncompactness 46b45 47b37 |
| url |
https://doi.org/10.1515/dema-2019-0015 |
| work_keys_str_mv |
AT ozgerfaruk characterizationsofcompactoperatorsonlptypefractionalsetsofsequences |
| _version_ |
1721347252513931264 |