Computable Banach spaces via domain theory

This paper extends the order-theoretic approach to computable analysis via continuous domains to complete metric spaces and Banach spaces. We employ t he domain of formal balls to define a computability theory for complete met ric spaces. For Banach spaces, the domain specialises to the domain of clos ed balls, ordered by reversed inclusion. We characterise computable linear operators as those which map computable sequences to computable sequences a nd are effectively bounded. We show that the domain-theoretic computability theory is equivalent to the well-established approach by Pour-El and Richa rds. (C) 1999 Published by Elsevier Science B.V. All rights reserved.