Dominated operators on \(C[0,1]\) and the (CRP). (English) Zbl 0752.47006

Emmanuele, Giovanni

Collect. Math. 41, No. 1, 21-25 (1990).

Summary: We show that a \(B\)-space \(E\) has the (CRP) if and only if any dominated operator \(T\) from \(C[0,1]\) into \(E\) is compact. Hence we apply this result to prove that \(c_ 0\) embeds isomorphically into the \(B\)-space of all compact operators from \(C[0,1]\) into an arbitrary \(B\)-space \(E\) without the \((CRP)\).

MSC:

47B07	Linear operators defined by compactness properties
47B38	Linear operators on function spaces (general)
47B25	Linear symmetric and selfadjoint operators (unbounded)
47B10	Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
46A32	Spaces of linear operators; topological tensor products; approximation properties

Keywords:

(CRP); dominated operator