On tensor products of nuclear operators in Banach spaces
The following result of G. Pisier contributed to the appearance of this paper: if a convolution operator ★f : M(G) → C(G), where $G$ is a compact Abelian group, can be factored through a Hilbert space, then f has the absolutely summable set of Fourier coefficients. We give some generalizations of th...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2021-12-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.onaft.edu.ua/index.php/geometry/article/view/2083 |
| _version_ | 1811330889126248448 |
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| author | Oleg Reinov |
| author_facet | Oleg Reinov |
| author_sort | Oleg Reinov |
| collection | DOAJ |
| description | The following result of G. Pisier contributed to the appearance of this paper: if a convolution operator ★f : M(G) → C(G), where $G$ is a compact Abelian group, can be factored through a Hilbert space, then f has the absolutely summable set of Fourier coefficients. We give some generalizations of the Pisier's result to the cases of factorizations of operators through the operators from the Lorentz-Schatten classes Sp,q in Hilbert spaces both in scalar and in vector-valued cases. Some applications are given. |
| first_indexed | 2024-04-13T16:09:43Z |
| format | Article |
| id | doaj.art-2d3b220407ea4874987ec3431cab8c12 |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-04-13T16:09:43Z |
| publishDate | 2021-12-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-2d3b220407ea4874987ec3431cab8c122022-12-22T02:40:17ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062021-12-0114318720510.15673/tmgc.v14i3.20832083On tensor products of nuclear operators in Banach spacesOleg ReinovThe following result of G. Pisier contributed to the appearance of this paper: if a convolution operator ★f : M(G) → C(G), where $G$ is a compact Abelian group, can be factored through a Hilbert space, then f has the absolutely summable set of Fourier coefficients. We give some generalizations of the Pisier's result to the cases of factorizations of operators through the operators from the Lorentz-Schatten classes Sp,q in Hilbert spaces both in scalar and in vector-valued cases. Some applications are given.https://journals.onaft.edu.ua/index.php/geometry/article/view/2083factorizationlorentz-schatten classnuclear operator |
| spellingShingle | Oleg Reinov On tensor products of nuclear operators in Banach spaces Pracì Mìžnarodnogo Geometričnogo Centru factorization lorentz-schatten class nuclear operator |
| title | On tensor products of nuclear operators in Banach spaces |
| title_full | On tensor products of nuclear operators in Banach spaces |
| title_fullStr | On tensor products of nuclear operators in Banach spaces |
| title_full_unstemmed | On tensor products of nuclear operators in Banach spaces |
| title_short | On tensor products of nuclear operators in Banach spaces |
| title_sort | on tensor products of nuclear operators in banach spaces |
| topic | factorization lorentz-schatten class nuclear operator |
| url | https://journals.onaft.edu.ua/index.php/geometry/article/view/2083 |
| work_keys_str_mv | AT olegreinov ontensorproductsofnuclearoperatorsinbanachspaces |