Skipped Blocking and other Decompositions in Banach spaces

Steven F. Bellenot

Necessary and sufficient conditions are given for when a sequence of finite dimensional subspaces $(X_n)$ can be blocked to be a skipped blocking decompositon ({\sf SBD}). These are very similar to known results about blocking of biorthogonal sequences. A separable space $X$ has {\sf PCP}, if and only if, every norming decomposition $(X_n)$ can be blocked to be a boundedly complete {\sf SBD}. Every boundedly complete {\sf SBD} is a {\sf JT}-decomposition.