Function Theory and $\ell ^p$ Spaces

William T. Ross, Javad Mashreghi, Raymond Cheng

ISBN 10: 1470455935 / ISBN 13: 9781470455934

Verlag: American Mathematical Society, US, 2020

Beschreibung

The classical $\ell^{p}$ sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces $\ell^{p}_{A}$ of analytic functions whose Taylor coefficients belong to $\ell^p$. Relations between the Banach space $\ell^p$ and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of $\ell^{p}_{A}$ and a discussion of the Wiener algebra $\ell^{1}_{A}$. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.

Bestandsnummer des Verkäufers LU-9781470455934

Bibliografische Details

• Titel: Function Theory and $\ell ^p$ Spaces
• Verlag: American Mathematical Society, US
• Veröffentlichungsdatum: 2020
• Sprache: Englisch
• ISBN-10: 1470455935
• ISBN-13: 9781470455934
• Bindung: Paperback
• Zustand: New

Über diesen Titel

Inhaltsangabe

The classical $\ell^{p}$ sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces $\ell^{p}_{A}$ of analytic functions whose Taylor coefficients belong to $\ell^p$. Relations between the Banach space $\ell^p$ and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of $\ell^{p}_{A}$ and a discussion of the Wiener algebra $\ell^{1}_{A}$. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.

Über die Autorin bzw. den Autor

Raymond Cheng,, Old Dominion University, Norfolk, VA

Javad Mashreghi, Laval University, Quebec City, QC, Canada

William T. Ross University of Richmond, VA