Extension of $c_0(I)$-valued operators on spaces of continuous functions on compact lines

Abstract

. We investigate the problem of existence of a bounded extension to C ( K ) of a bounded c 0 ( I )-valued operator T defined on the subalgebra of C ( K ) induced by a continuous increasing surjection φ : K → L , where K and L are compact lines. Generalizations of some of the results of [6] about extension of c 0 -valued operators are obtained. For instance, we prove that when a bounded extension of T exists then an extension can be obtained with norm at most twice the norm of T . Moreover, the class of compact lines L for which the c 0 -extension property is equivalent to the c 0 ( I )-extension property for any continuous increasing surjection φ : K → L is studied.