Some Automatic Continuity Theorems for Operator Algebras and\n Centralizers of Pedersen's Ideal

2014/04/10 by Lawrence G. Brown, Brown, Lawrence G.
Mathematics · #46L05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1404.2897

openalex publication_date 2014/04/10 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We prove automatic continuity theorems for "decomposable" or "local" linear\ntransformations between certain natural subspaces of operator algebras. The\ntransformations involved are not algebra homomorphisms but often are module\nhomomorphisms. We show that all left (respectively quasi-) centralizers of the\nPedersen ideal of a C*-algebra A are locally bounded if and only if A has no\ninfinite dimensional elementary direct summand. It has previously been shown by\nLazar and Taylor and Phillips that double centralizers of Pedersen's ideal are\nalways locally bounded.\n

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