2012/03/30 by Rogério Augusto dos Santos Fajardo, Rogério Fajardo, Fajardo, Rogério +5
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA
paper · pdf · doi:10.48550/arxiv.1203.6855
openalex publication_date 2012/03/30 · arxiv created 2012/08/03 · arxiv updated 2012/08/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We show that when C(K) does not have few operator -- in the sense of Koszmider [P. Koszmider, Banach spaces of continuous functions with few operators. Math. Ann. 300 (2004), no. 1, 151 - 183.] -- the sets of operators which are not weak multipliers is spaceable. This shows a contrast with what happens in general Banach spaces that do not have few operators. In addition, we show that there exist a C(K) space such that each operator on it is of the form gI+hJ+S, where g,h∈ C(K) and S is strictly singular, in connection to a result by Ferenczi [V. Ferenczi,Uniqueness of complex structure and real hereditarily indecomposable Banach spaces. Adv. Math. 213 (2007), no. 1, 462 - 488.].