Essentially Incomparable Banach Spaces of Continuous Functions

Spaces of continuous functions into a Banach space

Holomorphic functions on Banach spaces

This is a survey about some problems from the theory of holomorphic functions on Banach spaces which have attracted the attention of many researchers during the last thirty years.

Banach Spaces and Algebras of Continuous Functions1

Spaces of Continuous Functions

Let X be a completely regular topological space, B(X) the Banach space of real-valued bounded continuous functions on X, with the usual norm ||&|| =supa?£x|&(#)| • A subset GCB(X) is called completely regular (c.r.) over X if given any closed subset KQ.X and point XoÇzX — K, there exists a ô £ G such that &(#o) = |NI a n ( i sup^^is: \b(x)\ <||&||. A topological space X is completely regular in...

Banach and Fréchet spaces of functions

Many familiar and useful spaces of continuous or differentiable functions are Hilbert or Banach spaces, with pleasant completeness properties, but many are not. Some are Fréchet spaces, thus still complete, but lacking some of the conveniences of Banach spaces. Some other important spaces are not Fréchet, either. Still, some of these important spaces are colimits of Fréchet spaces (or of Banach...