Banach spaces without approximation properties of type p (original) (raw)

This note addresses a question concerning Banach spaces and their approximation properties of type p. It demonstrates that there exists a negative answer to the question posed in a previous paper regarding the existence of certain approximation properties in all Banach spaces. By reconstructing some results from earlier works, the note explicitly outlines conditions under which reflexive Banach spaces fail to exhibit the approximation property of type p, thereby extending the understanding of operator ideals associated with these spaces.