Hilbert空间中算子的直接极限

Nauka – Technika – Technologia. Tom 2 Pub Date : 1900-01-01 DOI:10.7494/978-83-66727-48-9_8

Wojciech Mikołajczyk

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引用次数: 0

摘要

本文给出了Segal-Bargmann空间上Toeplitz算子的直接(归纳)极限方法的一个应用。这个空间对应于一些无穷多变量的解析函数，它们对高斯测度是平方可积的。对于这样的算子有不同的方法，这些方法看起来是等价的，但会导致Toeplitz算子的不同性质。其中使用的工具是张量积，等距感应极限和框架。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Direct limits of operators in the Hilbert space

We present an application of the direct (inductive) limit approach to Toeplitz operators on Segal–Bargmann space. The space corresponds to some analytic functions of infinitely many variables that are square integrable with respect to a Gaussian measure. There are different approaches to such operators that only seem equivalent but lead to different properties of Toeplitz operators. Among the used tools are tensor products, isometric inductive limits and frames.

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Nauka – Technika – Technologia. Tom 2

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