Projectivity and lifting of Hilbert module maps
Copyright policy )Projectivity and lifting of Hilbert module maps
Summary: In a recent paper, Carlson, Foiaş, Williams and the author proved that isometric Hilbert modules are projective in the category of Hilbert modules similar to contractive ones. In this paper, a simple proof, based on a strengthened lifting theorem, is given. The proof also applies to an equivalent theorem of Foiaş and Williams on similarity to a contraction of a certain \(2\times 2\) operator matrix.
- University of Georgia Georgia
- University of Georgia Press United States
Structure theory of linear operators, category of Hilbert modules similar to contractive ones, Projective and injective objects in functional analysis, polynomially bounded, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), projective, Dilations, extensions, compressions of linear operators, similarity to a contraction, \(2\times 2\) operator matrix, lifting theorem, isometric Hilbert modules
Structure theory of linear operators, category of Hilbert modules similar to contractive ones, Projective and injective objects in functional analysis, polynomially bounded, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), projective, Dilations, extensions, compressions of linear operators, similarity to a contraction, \(2\times 2\) operator matrix, lifting theorem, isometric Hilbert modules
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!