Boundedly complete $M$-bases and complemented subspaces in Banach spaces
William J. Davis, Ivan Singer · Transactions of the American Mathematical Society · 1973
Subsequences of boundedly complete M-bases need not be boundedly complete. An example of a somewhat reflexive space is given whose dual and one of whose factors fail to be somewhat reflexive. A geometric description of boundedly complete M-bases is given which is equivalent to the definitions of V. D. Milman and W. B. Johnson. Finally, certain M-bases for separable spaces give rise to proper complemented subspaces.