Spaceability in sets of operators on

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. ition, we show that there exists a C ( K ) space on which each operator has the form g I + h J + S , where g , h ∈ C ( K ) and S is strictly singular, in connection to a result by Ferenczi (2007) [6].