Intersection Properties of Balls in Banach Spaces

Abstract EN

We introduce a weaker notion of central subspace called almost central subspace, and we study Banach spaces that belong to the class (GC), introduced by Veselý (1997).

In particular, we prove that if Y is an almost central subspace of a Banach space X such that Y is in the class (GC), then Y is a central subspace of X**.

We also prove that if Y is a semi M-ideal in a Banach space X such that Y⊥⊥ is an almost central subspace of X**, then Y is an M-ideal in X.

Certain stability results for quotient spaces, injective tensor product spaces, and polyhedral direct sums of Banach spaces are also derived.