On Positivity and Roots in Operator Algebras

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• 作者：Clifford A. Bearden (1)
  David P. Blecher (1)
  Sonia Sharma (2)
  
• 关键词：Primary 46L07 ; 47L30 ; 47B44 ; Secondary 47A60 ; 47A63 ; 47B65
• 刊名：Integral Equations and Operator Theory
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：79
• 期：4
• 页码：555-566
• 全文大小：349 KB
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• 作者单位：Clifford A. Bearden (1)
  David P. Blecher (1)
  Sonia Sharma (2)
  
  1. Department of Mathematics, University of Houston, Houston, TX, 77204-3008, USA
  2. Department of Mathematics, SUNY Cortland, Cortland, NY, 13045, USA
  
• ISSN：1420-8989

文摘

In earlier papers the second author and Charles Read have introduced and studied a new notion of positivity for operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. The present paper consists of complements to some facts in the just mentioned papers, concerning this notion of positivity. For example we prove a result on the numerical range of products of the roots of commuting operators with numerical range in a sector.