Banach Algebras on Semigroups and on Their Compactifications
| Author | : Harold G. Dales |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821847759 |
"Volume 205, number 966 (end of volume)."
Banach Algebras On Semigroups And On Their Compactifications
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Amenable Banach Algebras
| Author | : Volker Runde |
| Publisher | : Springer Nature |
| Total Pages | : 468 |
| Release | : 2020-03-03 |
| Genre | : Mathematics |
| ISBN | : 1071603515 |
This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability. Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter’s contents. Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.
Banach Function Algebras, Arens Regularity, and BSE Norms
| Author | : Harold Garth Dales |
| Publisher | : Springer Nature |
| Total Pages | : 452 |
| Release | : |
| Genre | : |
| ISBN | : 3031445325 |
Algebra in the Stone-Cech Compactification
| Author | : Neil Hindman |
| Publisher | : Walter de Gruyter |
| Total Pages | : 610 |
| Release | : 2011-12-23 |
| Genre | : Mathematics |
| ISBN | : 3110258358 |
This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Čech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory. There has been very active research in the subject dealt with by the book in the 12 years which is now included in this edition. This book is a self-contained exposition of the theory of compact right semigroups for discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.
Introduction to Banach Spaces and Algebras
| Author | : Graham R. Allan |
| Publisher | : Oxford University Press |
| Total Pages | : 380 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0199206538 |
A timely graduate level text in an active field covering functional analysis, with an emphasis on Banach algebras.
Banach Spaces of Continuous Functions as Dual Spaces
| Author | : H. G. Dales |
| Publisher | : Springer |
| Total Pages | : 286 |
| Release | : 2016-12-13 |
| Genre | : Mathematics |
| ISBN | : 3319323490 |
This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example. The study of C_0(K) has been an important area of functional analysis for many years. It gives several new constructions, some involving Boolean rings, of this space as well as many results on the Stonean space of Boolean rings. The book also discusses when Banach spaces of continuous functions are dual spaces and when they are bidual spaces.
The Analytical and Topological Theory of Semigroups
| Author | : Karl H. Hofmann |
| Publisher | : Walter de Gruyter |
| Total Pages | : 413 |
| Release | : 2011-05-03 |
| Genre | : Mathematics |
| ISBN | : 3110856042 |
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Complex Interpolation between Hilbert, Banach and Operator Spaces
| Author | : Gilles Pisier |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 92 |
| Release | : 2010-10-07 |
| Genre | : Mathematics |
| ISBN | : 0821848429 |
Motivated by a question of Vincent Lafforgue, the author studies the Banach spaces $X$ satisfying the following property: there is a function $\varepsilon\to \Delta_X(\varepsilon)$ tending to zero with $\varepsilon>0$ such that every operator $T\colon \ L_2\to L_2$ with $\T\\le \varepsilon$ that is simultaneously contractive (i.e., of norm $\le 1$) on $L_1$ and on $L_\infty$ must be of norm $\le \Delta_X(\varepsilon)$ on $L_2(X)$. The author shows that $\Delta_X(\varepsilon) \in O(\varepsilon^\alpha)$ for some $\alpha>0$ iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of $\theta$-Hilbertian spaces for some $\theta>0$ (see Corollary 6.7), where $\theta$-Hilbertian is meant in a slightly more general sense than in the author's earlier paper (1979).
Operator Algebras for Multivariable Dynamics
| Author | : Kenneth R. Davidson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 68 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821853023 |
Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.|Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.
Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space
| Author | : Zeng Lian |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 119 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821846566 |
The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.
