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.
Arvustused
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)
Part I. Topological structures and Banach algebras.- Part II. Algebraic structures.- Part III. The Appendix.- Bibliography.- Index.
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.
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