scratch
§ Banach Space That Does Not Admit Schrauder Basis
created 2023-04-02
- Schrauder basis is a basis where we can get all elements uniquely by taking countable sequence of elements from the basis.
- Apparently, every banach space that obeys the approximation property has countable basis.
- An example of a banach space without this properly was given in "a counterexample to the approximation problem in banach spaces" by Per Enflo.
- Thus, in no argument can we say "assume we have a (schrauder) basis..."
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