Markushevich basis
In geometry, a Markushevich basis is a biorthogonal system that is both complete and total. It can be described by the formulation:
Let be Banach space. A biorthogonal system in is a Markusevich basis if
and
Every Schauder basis of a Banach space is also a Markuschevich basis; the converse is not true in general. An example of a Markushevich basis that is not a Schauder basis is the set
in the space of complex continuous functions on whose values at 0 and 1 are equal, with the sup norm. It is an open problem whether or not every separable Banach space admits a Markushevich basis with for all.
