Weak products of complete pick spaces

Aleman, Alexandru (author): Lund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH

(creator_code:org_t)

Indiana University Mathematics Journal, 2021
2021
English 28 s.
In: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518. ; 70:1, s. 325-352

Related links:: http://dx.doi.org/10...; show more...; http://arxiv.org/pdf...; https://lup.lub.lu.s...; https://doi.org/10.1...; show less...

Abstract Subject headings

Let H be the Drury-Arveson or Dirichlet space of the unit ball of Cd. The weak product H ☉ H of H is the collection of all functions h that can be written as h =∑∞n=1 fngn, where ∑∞n=1 ||fn|| ||gn|| < ∞. We show that H ☉ H is contained in the Smirnov class of H; that is, every function in H ☉ H is a quotient of two multipliers of H, where the function in the denominator can be chosen to be cyclic in H . As a consequence, we show that the map N → closH ☉H N establishes a one-to-one and onto correspondence between the multiplier invariant subspaces of H and of H ☉ H . The results hold for many weighted Besov spaces H in the unit ball of Cd provided the reproducing kernel has the complete Pick property. One of our main technical lemmas states that, for weighted Besov spaces H that satisfy what we call the multiplier inclusion condition, any bounded column multiplication operator H → ⊕∞n=1 H induces a bounded row multiplication operator ⊕∞n=1 H → H . For the Drury-Arveson space Hd2 this leads to an alternate proof of the characterization of interpolating sequences in terms of weak separation and Carleson measure conditions.

By the author/editor: Aleman, Alexandr ...; Hartz, Michael; McCarthy, John E ...; Richter, Stefan

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.