2007/01/31 by Matthew Daws, Daws, Matthew
Mathematics · #46B70 #46H05 #46H15 #46L07 #47L25 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.FA #math.OA #msc:46B70 #msc:46H05 #msc:46H15 #msc:46L07 #msc:47L25
paper · pdf · doi:10.48550/arxiv.math/0701935
Latex, 13 pages; minor corrections; added reference to work of Uygul which shows the same result
openalex publication_date 2007/01/31 · arxiv created 2007/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A theorem of Davis, Figiel, Johnson and Pełczyński tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method, which has been adapted to the category of operator spaces by Xu, showing the this factorisation result also holds for completely bounded weakly-compact maps. In this note, we show that Xu's ideas can be adapted to give an intrinsic characterisation of when a completely contractive Banach algebra arises as a closed subalgebra of the algebra of completely bounded operators on a reflexive operator space. This result was shown by Young for Banach algebras, and our characterisation is a direct analogue of Young's, involving weakly almost periodic functionals.