Publication Date:
2013-09-13
Description:
Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra A , which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper, we do the same but now A is an algebra of operators on a Hilbert space. We briefly survey this noncommutative peak interpolation , which we have studied with coauthors in a long series of papers, and whose basic theory now appears to be approaching its culmination. This programme developed from, and is based partly on, theorems of Hay and Read whose proofs were spectacular, but therefore inaccessible to an uncommitted reader. We give short proofs of these results, using recent progress in noncommutative peak interpolation, and conversely give examples of the use of these theorems in peak interpolation. For example, we prove a useful new noncommutative peak interpolation theorem.
Print ISSN:
0024-6093
Electronic ISSN:
1469-2120
Topics:
Mathematics
