From axiomatics to intrinsic characterization: Some open problems in computable analysis

AbstractFive open problems are presented. The framework for these problems is the notion of a “computability structure” on a Banach space, which is discussed below. The study of Banach spaces — in particular, the study of Hilbert space — is an important topic in mathematics and its applications.Problems A and B are concerned with “transfer principles” for obtaining effective versions of classical theorems of mathematics. Problems C and D deal with separability and effective separability. Problem E is concerned with computability for classes of mathematical structures other than Banach spaces