Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators
The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from general...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/3989572 |
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doaj-190078996ca947bc954c820a5f399af52021-07-02T14:05:08ZengHindawi LimitedAdvances in Mathematical Physics1687-91392020-01-01202010.1155/2020/39895723989572Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal GeneratorsYoritaka Iwata0Faculty of ChemistryThe concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally unbounded infinitesimal generators. In conclusion, the concept of module over a Banach algebra is proposed as the generalization of the Banach algebra. As an application to mathematical physics, the rigorous formulation of a rotation group, which consists of unbounded operators being written by differential operators, is provided using the module over a Banach algebra.http://dx.doi.org/10.1155/2020/3989572 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yoritaka Iwata |
| spellingShingle |
Yoritaka Iwata Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators Advances in Mathematical Physics |
| author_facet |
Yoritaka Iwata |
| author_sort |
Yoritaka Iwata |
| title |
Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators |
| title_short |
Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators |
| title_full |
Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators |
| title_fullStr |
Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators |
| title_full_unstemmed |
Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators |
| title_sort |
theory of b(x)-module: algebraic module structure of generally unbounded infinitesimal generators |
| publisher |
Hindawi Limited |
| series |
Advances in Mathematical Physics |
| issn |
1687-9139 |
| publishDate |
2020-01-01 |
| description |
The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally unbounded infinitesimal generators. In conclusion, the concept of module over a Banach algebra is proposed as the generalization of the Banach algebra. As an application to mathematical physics, the rigorous formulation of a rotation group, which consists of unbounded operators being written by differential operators, is provided using the module over a Banach algebra. |
| url |
http://dx.doi.org/10.1155/2020/3989572 |
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AT yoritakaiwata theoryofbxmodulealgebraicmodulestructureofgenerallyunboundedinfinitesimalgenerators |
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1721328368153001984 |