On l1-Invariant Sequence Spaces

We introduce and investigate a new sectional property for topological sequence spaces, which we call the KB property. It turns out that multipliers into l∞ and multiplication by l1 play a very similar role for KB as multipliers into bs and multiplication by bv0 do for the well-known sectional property AB. However, we also encounter significant differences. One of these differences motivates the study of l1-invariant sequence spaces, that is, sequence spaces E with l1E = E.