Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel
Copyright policy )Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel
In this paper we solve a mapping problem for a particular class of Hilbert modules over an algebra multipliers of a diagonal Nevanlinna-Pick (NP) kernel. In this case, the regular representation provides a multiplier norm which induces the topology on the algebra. In particular, we show that, in an appropriate category, a certain class of Hilbert modules are projective. In addition, we establish a commutant lifting theorem for diagonal NP kernels.
- University of Florida United States
Projective and injective objects in functional analysis, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), commutant lifting theorem, diagonal Nevanlinna-Pick (NP) kernel, regular representation, Dilations, extensions, compressions of linear operators, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Hilbert modules
Projective and injective objects in functional analysis, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), commutant lifting theorem, diagonal Nevanlinna-Pick (NP) kernel, regular representation, Dilations, extensions, compressions of linear operators, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), 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).5 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).Top 10% 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!