Drury-Arveson 空间及其商空间中的算子理论与函数理论
泛函分析
2025-02-04 v7 复变函数
算子代数
摘要
Drury-Arveson 空间 ，也称为对称 Fock 空间或 -移位空间，是一个 Hilbert 函数空间，其上作用有一个自然的 -元组算子，从而赋予其 Hilbert 模的结构。本综述旨在介绍 Drury-Arveson 空间，全面展示该空间主要的算子理论和函数理论方面，并描述其在多变量算子理论和 Pick 插值理论中所扮演的普遍角色。
引用
@article{arxiv.1308.1081,
title = {Operator theory and function theory in Drury-Arveson space and its quotients},
author = {Michael Hartz and Orr Shalit},
journal= {arXiv preprint arXiv:1308.1081},
year = {2025}
}
备注
This is a significantly renewed version of the survey by Shalit that first appeared in 2014, with Hartz as a new co-author. The survey consists of a mildly updated version of the original survey together with an extensive survey incorporating new developments from the years 2014-2025 (to appear in the 2nd Edition of Operator Theory); 61 pages