## 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.
✦ LIBER ✦
Friedland–Hersonsky problem for matrix algebra
✍ Scribed by Wensheng Cao; Xiantao Wang
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 119 KB
- Volume
- 372
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we show that the answer to problem 3.9 in [Duke Math.
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In this article we classify rank-one nonincreasing maps ψ on n-square block triangular matrix algebras with the assumption that ψ(I n ) is of rank n. As applications, we obtain complete classifications of adjugate-commuting maps, and compound-commuting maps on block triangular matrix algebras.