Abstract
Five 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.
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