A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{\infty }\left({\mathbb{N}})
A family of commuting contraction semigroups (Pn(t))n∈N{\left({P}_{n}\left(t))}_{n\in {\mathbb{N}}}, defined on l1(N){l}^{1}\left({\mathbb{N}}), is presented. For this family, the product semigroup ∏n=1∞Pn(t){\prod }_{n=1}^{\infty }{P}_{n}\left(t) exists and has bounded generator. The infinite produ...
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De Gruyter
2025-07-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0168 |
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| author | Nieznaj Ernest |
| author_facet | Nieznaj Ernest |
| author_sort | Nieznaj Ernest |
| collection | DOAJ |
| description | A family of commuting contraction semigroups (Pn(t))n∈N{\left({P}_{n}\left(t))}_{n\in {\mathbb{N}}}, defined on l1(N){l}^{1}\left({\mathbb{N}}), is presented. For this family, the product semigroup ∏n=1∞Pn(t){\prod }_{n=1}^{\infty }{P}_{n}\left(t) exists and has bounded generator. The infinite product of the corresponding family of adjoint semigroups (Pn∗(t))n∈N{\left({P}_{n}^{\ast }\left(t))}_{n\in {\mathbb{N}}}, defined on l∞(N){l}^{\infty }\left({\mathbb{N}}), also exists and its generator is bounded. Explicit formulae for these generators are also given. |
| format | Article |
| id | doaj-art-e46f93a7461a4eb6b2a489c4fb0af1bb |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-e46f93a7461a4eb6b2a489c4fb0af1bb2025-08-20T03:50:00ZengDe GruyterOpen Mathematics2391-54552025-07-0123152454210.1515/math-2025-0168A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{\infty }\left({\mathbb{N}})Nieznaj Ernest0Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, PolandA family of commuting contraction semigroups (Pn(t))n∈N{\left({P}_{n}\left(t))}_{n\in {\mathbb{N}}}, defined on l1(N){l}^{1}\left({\mathbb{N}}), is presented. For this family, the product semigroup ∏n=1∞Pn(t){\prod }_{n=1}^{\infty }{P}_{n}\left(t) exists and has bounded generator. The infinite product of the corresponding family of adjoint semigroups (Pn∗(t))n∈N{\left({P}_{n}^{\ast }\left(t))}_{n\in {\mathbb{N}}}, defined on l∞(N){l}^{\infty }\left({\mathbb{N}}), also exists and its generator is bounded. Explicit formulae for these generators are also given.https://doi.org/10.1515/math-2025-0168infinite product of semigroups of operatorscontraction semigroupbounded generator47d0360j2760j35 |
| spellingShingle | Nieznaj Ernest A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{\infty }\left({\mathbb{N}}) Open Mathematics infinite product of semigroups of operators contraction semigroup bounded generator 47d03 60j27 60j35 |
| title | A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{\infty }\left({\mathbb{N}}) |
| title_full | A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{\infty }\left({\mathbb{N}}) |
| title_fullStr | A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{\infty }\left({\mathbb{N}}) |
| title_full_unstemmed | A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{\infty }\left({\mathbb{N}}) |
| title_short | A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{\infty }\left({\mathbb{N}}) |
| title_sort | family of commuting contraction semigroups on l1 n l 1 left mathbb n and l∞ n l infty left mathbb n |
| topic | infinite product of semigroups of operators contraction semigroup bounded generator 47d03 60j27 60j35 |
| url | https://doi.org/10.1515/math-2025-0168 |
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