The Paulsen Problem in operator theory

Abstract

The Paulsen Problem in Hilbert space frame theory has proved to be one of the most intractable problems in the field. We will help explain why by showing that this problem is equivalent to a fundamental, deep problem in operator theory. This answers a question posed by Bodmann and Casazza. We will also give generalizations of these problems and we will spell out exactly the complementary versions of the problem. Mathematics subject classification (2010): 42C15, 46C05.