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Bibasic Sequences and Norming Basic Sequences
It is shown that every infinite dimensional Banach space X contains a basic sequence $({x_n})$ having biorthogonal functionals $({f_n}) \subset {X^\ast }$ such that $({f_n})$ is also basic. If $[{f_n}]$ norms $[{x_n}]$ then $({f_n})$ is necessarily basic. If $[{f_n}]$ norms $[{x_n}]$ then $[{x_n}]$ norms $[{f_n}]$. In order that $[{f_n}]$ norms …