Centripetal operators and Koszmider spaces

We study properties of Koszmider spaces and introduce a related notion of weakly Koszmider spaces. We show that if the space K is weakly Koszmider and C(K) is isomorphic to C(L) then L is also weakly Koszmider, but the analogous result does not hold for Koszmider spaces. We also show that a connected Koszmider space is strongly rigid.