2011/10/27 by Narutaka Ozawa, Ozawa, Narutaka
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46H20 #Secondary 47L10 #math.FA #msc:46H20 #msc:47L10
paper · pdf · doi:10.48550/arxiv.1110.6216
3 pages
arxiv created 2011/10/27 · arxiv updated 2011/10/31
It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a result of Paulsen and Smith who proved the same for Banach algebras acting on Hilbert spaces.