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The Kadison–Singer problem for the direct sum of matrix algebras

✍ Scribed by Charles Akemann; Joel Anderson; Betul Tanbay

Book ID: 106504167
Publisher: Springer
Year: 2011
Tongue: English
Weight: 224 KB
Volume: 16
Category: Article
ISSN: 1385-1292
DOI: 10.1007/s11117-010-0109-1

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## Abstract We prove that matrix algebras over a Rickart __C__\*‐algebra are also Rickart __C__\*‐algebras. As a consequence of this, every Rickart __C__\*‐algebra is an __UMF__‐algebra and satisfies polar decomposition.