A Non-Reflexive Banach Space has Non-Smooth Third Conjugate Space
A Non-Reflexive Banach Space has Non-Smooth Third Conjugate Space
J. Dixmier has observed [3, p. 1070] that a non-reflexive Banach space has non-rotund fourth conjugate space. It is the aim of this paper to improve Dixmier’s result by showing that a non-reflexive Banach space already has non-smooth third conjugate space in that the images under natural embedding of the …