Topological Algebras And Their Applications
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| Author | : Alexander Katz |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 318 |
| Release | : 2018-05-07 |
| Genre | : Mathematics |
| ISBN | : 3110413558 |
Proceedings of the 8th International Conference of Topological Algebras and Their Applications (ICTAA-2014), held on May 26-30, 2014 in Playa de Villas de Mar Beach, dedicated to the memory of Anastasios Mallios (Athens, Greece). This series of conferences started in 1999 in Tartu, Estonia and were subsequently held in Rabat, Moroco (2000), Oulu, Finland (2001), Oaxaca, Mexico (2002), Bedlewo, Poland (2003), Athens, Greece (2005) and Tartu, Estonia (2008 and 2013). The topics of the conference include all areas of mathematics, connected with (preferably general) topological algebras and their applications, including all kinds of topological-algebraic structures as topological linear spaces, topological rings, topological modules, topological groups and semigroups; bornological-algebraic structures such as bornological linear spaces, bornological algebras, bornological groups, bornological rings and modules; algebraic and topological K-theory; topological module bundles, sheaves and others. Contents Some results on spectral properties of unital algebras and on the algebra of linear operators on a unital algebra Descriptions of all closed maximal one-sided ideals in topological algebras On non self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces Functional calculus on algebras of operators generated by a self-adjoint operator in Pontryagin space Π1 On Gelfand-Naimark type Theorems for unital abelian complex and real locally C*-, and locally JB-algebras Multipliers and strictly real topological algebras Multipliers in some perfect locally m-pseudo-convex algebras Wedderburn structure theorems for two-sided locally m-convex H*-algebras Homologically best modules in classical and quantized functional analysis Operator Grüss inequality Main embedding theorems for symmetric spaces of measurable functions Mapping class groups are linear Subnormable A-convex algebras Commutative BP*-algebras and Gelfand-Naimark’s theorem Discrete nonclosed subsets in maximally nondiscrete topological groups Faithfully representable topological *-algebras: some spectral properties On continuity of complementors in topological algebras Dominated ergodic theorem for isometries of non-commutative Lp-spaces, 1 p p ≠ 2 Ranks and the approximate n-th root property of C*-algebras Dense ideals in topological algebras: some results and open problems
| Author | : Hugo Arizmendi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 152 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821835564 |
The Fourth International Conference on Topological Algebras and Their Applications was held in Oaxaca, Mexico. This meeting brought together international specialists and Mexican specialists in topological algebras, locally convex and Banach spaces, spectral theory, and operator theory and related topics. This volume contains talks presented at the conference as well as articles received in response to a call for papers; some are expository and provide new insights, while others contain new research. The book is suitable for graduate students and research mathematicians working in topological vector spaces, topological algebras, and their applications.
| Author | : M. Fragoulopoulou |
| Publisher | : Elsevier |
| Total Pages | : 514 |
| Release | : 2005-07-26 |
| Genre | : Mathematics |
| ISBN | : 0080461220 |
This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common.Key features:- Lucid presentation- Smooth in reading- Informative- Illustrated by examples- Familiarizes the reader with the non-normed *-world- Encourages the hesitant- Welcomes new comers.- Well written and lucid presentation.- Informative and illustrated by examples.- Familiarizes the reader with the non-normed *-world.
| Author | : S. Lefschetz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 190 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468493671 |
This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.
| Author | : Michael Farber |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 202 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821842463 |
Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.
| Author | : J. P. May |
| Publisher | : University of Chicago Press |
| Total Pages | : 262 |
| Release | : 1999-09 |
| Genre | : Mathematics |
| ISBN | : 9780226511832 |
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
| Author | : Anastasios Mallios |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 466 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821838687 |
The Fifth International Conference on Topological Algebras and Applications was held in Athens, Greece, from June 27th to July 1st of 2005. The main topic of the Conference was general theory of topological algebras and its various applications, with emphasis on the ``non-normed'' case. in addition to the study of the internal structure of non-normed, and even non-locally convex topological algebras, there are applications to other branches of mathematics, such as differential geometry of smooth manifolds, and mathematical physics, such as quantum relativity and quantum cosmology. Operator theory of unbounded operators and related non-normed topological algebras are intensively studied here. Other topics presented in this volume are topological homological algebra, topological algebraic geometry, sheaf theory and $K$-theory.
| Author | : Werner Ghler |
| Publisher | : World Scientific |
| Total Pages | : 378 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9789812702418 |
The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich OCo one of the leading category theorists of the world OCo to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst HerrlichOCOs publications. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."
| Author | : Tomás Domínguez Benavides |
| Publisher | : Universidad de Sevilla |
| Total Pages | : 184 |
| Release | : 1996 |
| Genre | : Education |
| ISBN | : 9788447203505 |
| Author | : J-P Antoine |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 554 |
| Release | : 2002-12-31 |
| Genre | : Mathematics |
| ISBN | : 9781402010255 |
Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algebras of unbounded operators (O*-algebras), mostly developed by the Leipzig school and in Japan (for a review, we refer to the monographs of K. Schmüdgen [1990] and A. Inoue [1998]). This volume goes one step further, by considering systematically partial *-algebras of unbounded operators (partial O*-algebras) and the underlying algebraic structure, namely, partial *-algebras. It is the first textbook on this topic. The first part is devoted to partial O*-algebras, basic properties, examples, topologies on them. The climax is the generalization to this new framework of the celebrated modular theory of Tomita-Takesaki, one of the cornerstones for the applications to statistical physics. The second part focuses on abstract partial *-algebras and their representation theory, obtaining again generalizations of familiar theorems (Radon-Nikodym, Lebesgue).
