This is an announcement for the paper "Effective Banach spaces" by Bjorn Kjos-Hanssen. Abstract: 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. Archive classification: math.LO math.FA Mathematics Subject Classification: 03D Remarks: Master's thesis, University of Oslo, 1997. Adviser: Dag Normann. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.6622 or http://arXiv.org/abs/1207.6622