| 书目名称 | Index Theory Beyond the Fredholm Case |
| 编辑 | Alan Carey,Galina Levitina |
| 视频video | |
| 概述 | Provides an overview of double operator integrals‘emerging as a valuable tool in non-commutative analysis.Presents‘new material on a generalisation of the notion of spectral flow for non- Fredholm ope |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | This book is about extending index theory to some examples where non-Fredholm operators arise. It focuses on one aspect of the problem of what replaces the notion of spectral flow and the Fredholm index when the operators in question have zero in their essential spectrum. Most work in this topic stems from the so-called Witten index that is discussed at length here. The new direction described in these notes is the introduction of `spectral flow beyond the Fredholm case‘..Creating a coherent picture of numerous investigations and scattered notions of the past 50 years, this work carefully introduces spectral flow, the Witten index and the spectral shift function and describes their relationship. After the introduction, Chapter 2 carefully reviews Double Operator Integrals, Chapter 3 describes the class of so-called p-relative trace class perturbations, followed by the construction of Krein‘s spectral shift function in Chapter 4. Chapter 5 reviews the analytic approach to spectral flow, culminating in Chapter 6 in the main abstract result of the book, namely the so-called principal trace formula. Chapter 7 completes the work with illustrations of the main results using explicit comp |
| 出版日期 | Book 2022 |
| 关键词 | Witten Index; Spectral Shift Function; Double Operator Integrals; Spectral Flow; Robbin-Salaman Theorem |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-19436-8 |
| isbn_softcover | 978-3-031-19435-1 |
| isbn_ebook | 978-3-031-19436-8Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 19:31:20
