Extension Problems and Stable Ranks

Beschreibung

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.

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.


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

Autor*in

Raymond Mortini

Themen in »Extension Problems and Stable Ranks«

topological spaces compact sets and continua function spaces and function algebras Hardy spaces Banach algebras continuous functions holomorphic functions almost periodic functions extension problems interpolation and approximation problems dbar-calculus Bézout equation Corona-theorem Bass stable rank topological stable rank

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“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)
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