Weakly compact operators and strict topologies

作者：Nowak Marian^*

来源：Topology and Its Applications, 2013, 160(16): 2053-2060.

DOI：10.1016/j.topol.2013.08.011

• Spaces of bounded continuous functions
• Strict topologies
• Weakly compact operators
• Tight operators
• tau-additive operators
• sigma-additive operators
• Vector measures
• Baire measures

Let X be a completely regular Hausdorff space and C-b(X) be the Banach space of all real-valued bounded continuous functions on X, endowed with the uniform norm. It is shown that every weakly compact operator T from C-b(X) to a quasicomplete locally convex Hausdorff space E can be uniquely decomposed as T = T-1 + T-2 + T-3 + T-4 where T-k : C-b(X) -> E (k = 1,2,3,4) are weakly compact operators, and T-1 is tight, T-2 is purely tau-additive, T-3 is purely sigma-additive and T-4 is purely finitely additive. Moreover, we derive a generalized Yosida-Hewitt decomposition for E-valued strongly bounded regular Baire measures.

• 出版日期2013-10-1