Distance between reproducing kernel Hilbert spaces and geometry of finite sets in the unit ball

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:500

Article

Ofek, Danny¹  Pandey, Satish K.²  Shalit, Orr Moshe² 

[1] Tel Aviv Univ, Sch Math Sci, IL-6997801 Tel Aviv, Israel

[2] Technion Israel Inst Technol, Fac Math, IL-3200003 Haifa, Israel

关键词: Reproducing kernel Hilbert spaces;    Multiplier algebras;    Reproducing kernel Banach-Mazur distance;    Multiplier Banach-Mazur distance;   

DOI  :  10.1016/j.jmaa.2021.125140

来源: Elsevier

【 摘 要 】

In this paper we study the relationships between a reproducing kernel Hilbert space, its multiplier algebra, and the geometry of the point set on which they live. We introduce a variant of the Banach-Mazur distance suited for measuring the distance between reproducing kernel Hilbert spaces, that quantifies how far two spaces are from being isometrically isomorphic as reproducing kernel Hilbert spaces. We introduce an analogous distance for multiplier algebras, that quantifies how far two algebras are from being completely isometrically isomorphic. We show that, in the setting of finite dimensional quotients of the Drury-Arveson space, two spaces are close to one another if and only if their multiplier algebras are close, and that this happens if and only if one of the underlying point sets is close to an image of the other under a biholomorphic automorphism of the unit ball. These equivalences are obtained as corollaries of quantitative estimates that we prove. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free