Mathematical Sciences: "Applications of Extension Theorems on Krein Spaces"

数学科学：“可拓定理在 Kerin 空间上的应用”

• 批准号: 9002469
• 负责人: E. Zachmanoglou
• 金额: $ 3.22万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002469&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Extension; Theorems

This research explores various applications of the extension theorems and commutant lifting theorems for contraction operators on Krein spaces. Some of these problems, such as the Krein space formulation of Foias' generalization of an interpolation problem of Dym and Gohberg, are natural restatements of classical Hilbert space problems. Other of these problems, such as the study of maximal negative subspaces of bicontractive operators, make sense only within the context of indefinite inner product spaces. This research is in the general area of modern analysis. Its focus is on the commutant lifting theorems for certain classes of operators on Krein spaces. For Hilbert space contractions, the lifting theorem has been well known since the late 1960's and has been a powerful tool in areas such as classical interpolation theory and in corona theory.

本研究探讨了 Kerin 空间上收缩算子的可拓定理和交换提升定理的各种应用。 其中一些问题，例如 Foias 对 Dym 和 Gohberg 插值问题的推广的 Kerin 空间公式，是经典希尔伯特空间问题的自然重述。其他这些问题，例如双收缩算子的最大负子空间的研究，只有在不定内积空间的背景下才有意义。 这项研究属于现代分析的一般领域。 它的重点是 Kerin 空间上某些类别算子的交换提升定理。 对于希尔伯特空间收缩，提升定理自 20 世纪 60 年代末以来就广为人知，并且一直是经典插值理论和日冕理论等领域的强大工具。