Some Automatic Continuity Theorems for Operator Algebras and Centralizers of Pedersen’s Ideal

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• 作者：Lawrence G. Brown
• 关键词：Pedersen’s ideal ; Centralizer ; Multiplier ; Automatic continuity
• 刊名：Integral Equations and Operator Theory
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：86
• 期：2
• 页码：249-270
• 全文大小：645 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989
• 卷排序：86

文摘

We prove automatic continuity theorems for “decomposable” or“local” linear transformations between certain natural subspaces of operator algebras. The transformations involved are not algebra homomorphisms but often are module homomorphisms. We show that all left (respectively quasi-) centralizers of the Pedersen ideal of a C*-algebra A are locally bounded if and only if A has no infinite dimensional elementary direct summand. It has previously been shown by Lazar and Taylor and Phillips that double centralizers of Pedersen’s ideal are always locally bounded.