On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space
We prove that if E is a Dedekind complete atomless Riesz space and X is a Banach space, then the sum of two laterally continuous orthogonally additive operators from E to X, one of which is strictly narrow and the other one is hereditarily strictly narrow with finite variation (in particular, has fi...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/8569409 |
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| _version_ | 1832548760781062144 |
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| author | Oleksandr Maslyuchenko Mikhail Popov |
| author_facet | Oleksandr Maslyuchenko Mikhail Popov |
| author_sort | Oleksandr Maslyuchenko |
| collection | DOAJ |
| description | We prove that if E is a Dedekind complete atomless Riesz space and X is a Banach space, then the sum of two laterally continuous orthogonally additive operators from E to X, one of which is strictly narrow and the other one is hereditarily strictly narrow with finite variation (in particular, has finite rank), is strictly narrow. Similar results were previously obtained for narrow operators by different authors; however, no theorem of the kind was known for strictly narrow operators. |
| format | Article |
| id | doaj-art-544ad5cfd43e4380bb2bf54dee369a9a |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-544ad5cfd43e4380bb2bf54dee369a9a2025-02-03T06:13:08ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/85694098569409On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach SpaceOleksandr Maslyuchenko0Mikhail Popov1Institute of Mathematics, University of Silesia in Katowice, Bankowa 12, 40-007 Katowice, PolandInstitute of Mathematics, Pomeranian University in Słupsk, ul. Arciszewskiego 22d, 76-200 Słupsk, PolandWe prove that if E is a Dedekind complete atomless Riesz space and X is a Banach space, then the sum of two laterally continuous orthogonally additive operators from E to X, one of which is strictly narrow and the other one is hereditarily strictly narrow with finite variation (in particular, has finite rank), is strictly narrow. Similar results were previously obtained for narrow operators by different authors; however, no theorem of the kind was known for strictly narrow operators.http://dx.doi.org/10.1155/2019/8569409 |
| spellingShingle | Oleksandr Maslyuchenko Mikhail Popov On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space Journal of Function Spaces |
| title | On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space |
| title_full | On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space |
| title_fullStr | On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space |
| title_full_unstemmed | On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space |
| title_short | On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space |
| title_sort | on sums of strictly narrow operators acting from a riesz space to a banach space |
| url | http://dx.doi.org/10.1155/2019/8569409 |
| work_keys_str_mv | AT oleksandrmaslyuchenko onsumsofstrictlynarrowoperatorsactingfromarieszspacetoabanachspace AT mikhailpopov onsumsofstrictlynarrowoperatorsactingfromarieszspacetoabanachspace |