Finite dimensional semisimple Q-algebras


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Please use this identifier to cite or link to this item:http://hdl.handle.net/2115/17154

Title:	Finite dimensional semisimple Q-algebras
Authors:	Nakazi, Takahiko Browse this author
Authors:	Yamamoto, Takanori Browse this author
Keywords:	Commutative Banach algebra
	Semisimple Q-algebra
	Three dimension
	Norm
	Pick interpolation
Issue Date:	15-Jan-2007
Publisher:	Elsevier Inc.
Journal Title:	Linear Algebra and its Applications
Volume:	420
Issue:	2-3
Start Page:	407
End Page:	423
Publisher DOI:	10.1016/j.laa.2006.07.016
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.
Relation:	http://www.sciencedirect.com/science/journal/00243795
Type:	article (author version)
URI:	http://hdl.handle.net/2115/17154
Appears in Collections:	理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 中路貴彦

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