Skip to main content
SpringerLink
Log in
Birkhäuser

Extension Problems and Stable Ranks

A Space Odyssey

  • Book
  • © 2021

Overview

Authors:
  1. Raymond Mortini

    1. CNRS, IECL, Université de Lorraine, Metz, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Rudolf Rupp

    1. Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, Technische Hochschule Nürnberg, Georg Simon Ohm, Nürnberg, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • The first monograph on the Bass and topological stable rank for analysts
  • Contains all relevant material written in an easily readable way to attack problems in this very active domain
  • Gives an introduction to topology and Banach algebras, featuring, in particular, real Banach algebras
  • Presents several advanced topics in complex analysis, thus accessible also for students and lecturers, and a good basis for seminars and advanced courses

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 229.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 299.99
Price excludes VAT (USA)
This title has not yet been released. You may pre-order it now and we will ship your order when it is published on 29 Oct 2022.
  • Compact, lightweight edition
  • Free shipping worldwide - see info
Hardcover Book USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (36 chapters)

  1. Algebraic structures

    1. Front Matter

      Pages 1073-1073
      Download chapter PDF

    2. Algebraic preliminaries

      • Raymond Mortini, Rudolf Rupp
      Pages 1074-1091

    3. The Bézout equation

      • Raymond Mortini, Rudolf Rupp
      Pages 1092-1115

    4. The algebras Cb(X,\( \mathbb{K} \)) and C(X,\( \mathbb{K} \)) on non-compact spaces

      • Raymond Mortini, Rudolf Rupp
      Pages 1116-1152

    5. Polynomial, Noetherian, and von Neumann regular rings

      • Raymond Mortini, Rudolf Rupp
      Pages 1153-1194

    6. The Bass and topological stable ranks

      • Raymond Mortini, Rudolf Rupp
      Pages 1195-1247

    7. The stable ranks for algebras of polynomials and entire functions

      • Raymond Mortini, Rudolf Rupp
      Pages 1248-1262

    8. The Bass and topological stable ranks of C(X,\( \mathbb{K} \))

      • Raymond Mortini, Rudolf Rupp
      Pages 1263-1308

    9. The planar algebras P(K), R(K), A(K), C(K), and their siblings

      • Raymond Mortini, Rudolf Rupp
      Pages 1309-1412

    10. The algebra of bounded analytic functions

      • Raymond Mortini, Rudolf Rupp
      Pages 1413-1581

    11. Peak sets in function algebras

      • Raymond Mortini, Rudolf Rupp
      Pages 1582-1603

    12. Lipschitz algebras

      • Raymond Mortini, Rudolf Rupp
      Pages 1604-1632

    13. Regular and normal Banach algebras

      • Raymond Mortini, Rudolf Rupp
      Pages 1633-1646

    14. The stable ranks for a zoo of algebras

      • Raymond Mortini, Rudolf Rupp
      Pages 1647-1700

    15. Various notions of reducibility and stable ranks

      • Raymond Mortini, Rudolf Rupp
      Pages 1701-1793

    16. Stable ranks of holomorphic function algebras in \( \mathbb{C}^{n} \)

      • Raymond Mortini, Rudolf Rupp
      Pages 1794-1822

    17. Real-symmetric function algebras

      • Raymond Mortini, Rudolf Rupp
      Pages 1823-1876

    18. The algebra of almost periodic functions

      • Raymond Mortini, Rudolf Rupp
      Pages 1877-1954

    19. Matricial stable ranks

      • Raymond Mortini, Rudolf Rupp
      Pages 1955-1998

  2. Back Matter

    Pages 1999-2176
    Download chapter PDF
Back to top

Keywords

About this book

This self-contained encyclopedic monograph gives a detailed introduction to Bézout equations and stable ranks, encompassing and explaining needed topological, analytical, and algebraic tools and methods. Some of the highlights included are Carleson's corona theorem and the Bass, topological, and matricial stable ranks.

The first volume focusses on topological structures, Banach algebras, and advanced function theory, thus preparing the stage for the algebraic structures in the second volume towards examining stable ranks with analytic methods. The main emphasis is laid on algebras of holomorphic functions. Often a new approach is presented or at least a different angle of sight, which makes the book attractive both for researchers and students interested in these active fields of research.


Reviews

“The book under review is a self-contained monograph which gives a thorough overview of facts and results that are needed in order to understand the proofs of the results about extension problems and standard ranks. ... The book is a good resource for scientists working on stable ranks and extension problems and is also accessible to advanced graduate students.” (Mart Abel, zbMATH 1516.46002, 2023)

“The work under review is an encyclopedic two-volume treatise … . The book is clearly written and quite detailed, and includes an extensive bibliography, historical notes and an index.” (Michael T. Jury, Mathematical Reviews, October, 2023)

Authors and Affiliations

  • CNRS, IECL, Université de Lorraine, Metz, France

    Raymond Mortini

  • Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, Technische Hochschule Nürnberg, Georg Simon Ohm, Nürnberg, Germany

    Rudolf Rupp

About the authors

RAYMOND MORTINI, born 1958, is professor emeritus at the Université de Lorraine in Metz (France) and, since 2020, guest researcher at the University of Luxembourg, his home country. He obtained his Ph.D. (1984) and habilitation (1988) at the University of Karlsruhe (Germany) and was hired by the Université de Metz in 1995. From 2017-2020 he hold his courses at the University of Luxembourg, still being affiliated with the Université de Lorraine. His main interests lie in function theory, functional analysis, operator theory and point set topology. Currently he is in the editorial board of three Springer journals. 

RUDOLF RUPP, born 1960, is professor at the Nuremberg Institute of Technology, Georg-Simon-Ohm in Nuremberg, Germany. He obtained his Ph.D.(1988) and habilitation (1992) at the University of Karlsruhe (Germany), now called KIT. From 1999 until 2003 he persued a job outside the university. His research interests lie in function theory, Banach algebras and point set topology.


Bibliographic Information

  • Book Title: Extension Problems and Stable Ranks

  • Book Subtitle: A Space Odyssey

  • Authors: Raymond Mortini, Rudolf Rupp

  • DOI: https://doi.org/10.1007/978-3-030-73872-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-73871-6Published: 03 August 2021

  • eBook ISBN: 978-3-030-73872-3Published: 02 August 2021

  • Edition Number: 1

  • Number of Pages: XXII, 2176

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Functions of a Complex Variable, Functional Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation