Spaceability in sets of operators on C(K)

作者：Fajardo Rogerio; Kaufmann Pedro L; Pellegrini Leonardo^*

来源：Topology and Its Applications, 2013, 160(2): 387-393.

DOI：10.1016/j.topol.2012.11.017

• Spaceability
• Few operators
• Banach space of continuous functions

We show that when C(K) does not have few operators - in the sense of Koszmider (2004) [8] - the set of operators which are not weak multipliers is spaceable. That is, there exists an infinite-dimensional space of operators on C(K), each nonzero element of which is not a weak multiplier. This contrasts to what happens in general Banach spaces that do not have few operators.
In addition, we show that there exists a C(K) space on which each operator has the form gI + hJ + S, where g, h is an element of C(K) and S is strictly singular, in connection to a result by Ferenczi (2007) [6].

• 出版日期2013-2-1