Finite representability of operators

We introduce operator local supportability as a new type of operator finite representability that generalizes Bellenot finite representability. We prove that local supportability and local representability are mutually independent. New examples of both types of finite representability are given. For instance, for every operator T , we prove that (TU)∗ is locally supportable in (T ∗)U. We also prove that, given an operator T with range in C[0, 1], T ∗ is locally representable in T ∗|L1 .  2003 Elsevier Science (USA). All rights reserved