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Finite dimensional semisimple Q-algebras

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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
Pick interpolation
Issue Date: 2006
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)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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