Effective Banach spaces
  This thesis addresses Pour-El and Richards' fourth question from their book "Computability in analysis and physics", concerning the relation between higher order recursion theory and computability in analysis.   Among other things it is shown that there is a computability structure that is uncountable. The example given is a structure on the Banach space of bounded linear operators on the set of almost periodic functions. 
Bj{\o}rn Kjos-Hanssen
math.LO math.FA