Markuschevich bases and duality theory Academic Article uri icon


  • Several duality theorems concerning Schauder bases in locally convex spaces have analogues in the theory of Markuschevich bases. For example, a locally convex space with a Markuschevich basis is semireflexive iff the basis is shrinking and boundedly complete. The strong existence Theorem III.1 for Markuschevich bases allows us to show that a separable Banach space is isomorphic to a conjugate space iff it admits a boundedly complete Markuschevich basis, and that a separable Banach space has the metric approximation property iff it admits a Markuschevich basis which is a generalized summation basis in the sense of Kadec.

published proceedings

  • Transactions of the American Mathematical Society

author list (cited authors)

  • Johnson, W. B.

citation count

  • 7

complete list of authors

  • Johnson, William B

publication date

  • January 1970