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Hokkaido University Preprint Series in Mathematics >
Finite dimensional semisimple Q-algebras
| Title: | Finite dimensional semisimple Q-algebras |
| Authors: | Nakazi, Takahiko Browse this author | | Yamamoto, Takanori Browse this author |
| Keywords: | commutative Banach algebra | | semisimple Q-algebra | | three dimension | | norm | | Pick interpolation |
| Issue Date: | 2006 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 793 |
| Start Page: | 1 |
| End Page: | 17 |
| Abstract: | A Q-algebra can be represented as an operator algebra on an infinite dimensional Hilbert space. However we don't know whether a finite n-dimensional Q-algebra can be represented on a Hilbert space of dimension n except n = 1, 2. It is known that a two dimensional Q-algebra is just a two dimensional commutative operator algebra on a two dimensional Hilbert space. In this paper we study a finite n-dimensional semisimple Q-algebra on a finite n-dimensional Hilbert space. In particular we describe a three dimensional Q-algebra of the disc algebra on a three dimensional Hilbert space. Our studies are related to the Pick interpolation problem for a uniform algebra. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69601 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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