On the existence of a cyclic vector of some families of operators
It is proved that, under some restrictions, a family of selfadjoint commuting operators A=(Aφ) φ ∈ Φ where Φ is a nuclear space, has a cyclic vcctor iff there exists a Hilbert space H ⊂ Φ′ of full operator-valued measure E, where Φ′ is the dual of Φ, E is the joint resolution of the identity of the...
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| Published in: | Український математичний журнал |
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| Date: | 1993 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
1993
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155297 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the existence of a cyclic vector of some families of operators / E. V. Lytvynov // Український математичний журнал. — 1993. — Т. 45, № 10. — С. 1362–1370.. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708266769842176 |
|---|---|
| author | Lytvynov, E. V. |
| author_facet | Lytvynov, E. V. |
| citation_txt | On the existence of a cyclic vector of some families of operators / E. V. Lytvynov // Український математичний журнал. — 1993. — Т. 45, № 10. — С. 1362–1370.. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний журнал |
| description | It is proved that, under some restrictions, a family of selfadjoint commuting operators A=(Aφ) φ ∈ Φ where Φ is a nuclear space, has a cyclic vcctor iff there exists a Hilbert space H ⊂ Φ′ of full operator-valued measure E, where Φ′ is the dual of Φ, E is the joint resolution of the identity of the family A.
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| first_indexed | 2025-12-07T17:10:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155297 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1027-3190 |
| language | English |
| last_indexed | 2025-12-07T17:10:48Z |
| publishDate | 1993 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lytvynov, E. V. 2019-06-16T15:42:06Z 2019-06-16T15:42:06Z 1993 On the existence of a cyclic vector of some families of operators / E. V. Lytvynov // Український математичний журнал. — 1993. — Т. 45, № 10. — С. 1362–1370.. — Бібліогр.: 7 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/155297 517.515 It is proved that, under some restrictions, a family of selfadjoint commuting operators A=(Aφ) φ ∈ Φ where Φ is a nuclear space, has a cyclic vcctor iff there exists a Hilbert space H ⊂ Φ′ of full operator-valued measure E, where Φ′ is the dual of Φ, E is the joint resolution of the identity of the family A. en Інститут математики НАН України Український математичний журнал Статті On the existence of a cyclic vector of some families of operators Про існування циклічного вектора деяких сімей операторів Article published earlier |
| spellingShingle | On the existence of a cyclic vector of some families of operators Lytvynov, E. V. Статті |
| title | On the existence of a cyclic vector of some families of operators |
| title_alt | Про існування циклічного вектора деяких сімей операторів |
| title_full | On the existence of a cyclic vector of some families of operators |
| title_fullStr | On the existence of a cyclic vector of some families of operators |
| title_full_unstemmed | On the existence of a cyclic vector of some families of operators |
| title_short | On the existence of a cyclic vector of some families of operators |
| title_sort | on the existence of a cyclic vector of some families of operators |
| topic | Статті |
| topic_facet | Статті |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155297 |
| work_keys_str_mv | AT lytvynovev ontheexistenceofacyclicvectorofsomefamiliesofoperators AT lytvynovev proísnuvannâciklíčnogovektoradeâkihsímeioperatorív |