Renormings in Banach Spaces: A Toolbox

This monograph provides an up-to-date overview of renorming in Banach spaces, covering convexity, differentiability, equivalent norms, and its applications. It serves as a text for advanced courses, a reference for specialists, and a gateway to the field for newcomers. It offers a flexible approach, from in-depth proofs to useful results, and includes open problems and discussions to encourage research.

Format: Hardback
Length: 625 pages
Publication date: 24 August 2022
Publisher: Birkhauser Verlag AG

This comprehensive monograph provides a thorough and up-to-date overview of the diverse techniques and remarkable outcomes in the vast realm of renorming in Banach spaces, along with their numerous applications. It serves as a self-contained exposition, presenting the fundamental concepts of convexity and differentiability, classical results in establishing equivalent norms with practical properties, and the evolution of the subject from its early origins to the present day. Emphasis is placed on elucidating the core ideas and their interconnectedness, making the content accessible to both experts and newcomers to the field.

The book encompasses several objectives. Firstly, it serves as a valuable text for advanced courses in the geometry of Banach spaces, presenting results, proofs, and comprehensive discussions in a structured manner. Secondly, it serves as a comprehensive reference, offering a vast collection of recent contributions that highlight the current state-of-the-art in the field. Thirdly, it caters to both specialists and newcomers by presenting the content in a way that enables ready access to useful results without delving into intricate details. This flexible approach, spanning from in-depth proof reading to searching for practical applications, is maintained throughout the book. Additionally, open problems and discussions are included, fostering the ongoing advancement of this active and dynamic area of research.

In summary, this monograph offers a comprehensive and accessible guide to the field of renorming in Banach spaces, presenting a wealth of knowledge and insights for both experts and enthusiasts. Its self-contained nature, extensive coverage, and flexible approach make it an invaluable resource for anyone interested in this dynamic and rapidly evolving area of mathematics.

Weight: 1136g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031086540
Edition number: 1st ed. 2022