Topological direct sum decompositions of Banach spaces (Q1173837)

The author proves several results on the existence of direct sum decompositions in Banach spaces. The climax of these results asserts that every Banach space \(X\) has a decomposition: \(X= X_{\text{ref}} \oplus X_{\text{rad}}\) with \(X_{\text{ref}}\) reflexive and \(\text{dens } X^{**}_{\text{rad}}= \text{dens } X^{**}/ X\). This result was previously obtained by the author [Stud. Math. 60, No. 1, 11-13 (1977; Zbl 0354.46012)] in the case in which \(X^{**}/ X\) is separable.