Ozawa, Narutaka 1974
Overview
Works:  4 works in 13 publications in 1 language and 274 library holdings 

Roles:  Author, 958, Opponent 
Publication Timeline
.
Most widely held works by
Narutaka Ozawa
C*algebras and finitedimensional approximations by
Nathanial P Brown(
Book
)
10 editions published between 2006 and 2008 in English and held by 270 WorldCat member libraries worldwide
"C*approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains userfriendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applicationswritten with researchers and advanced, welltrained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of C*approximation theory."Publisher's description
10 editions published between 2006 and 2008 in English and held by 270 WorldCat member libraries worldwide
"C*approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains userfriendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applicationswritten with researchers and advanced, welltrained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of C*approximation theory."Publisher's description
Local theory and local reflexivity for operator spaces by
Narutaka Ozawa(
)
1 edition published in 2001 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 2 WorldCat member libraries worldwide
Amenable actions and applications by
Narutaka Ozawa(
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Théorie ergodique des actions de groupes et algèbres de von Neumann by
Alessandro Carderi(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This dissertation is about measured group theory, sofic entropy and operator algebras. More precisely, we will study actions of groups on probability spaces, some fundamental properties of their sofic entropy (for countable groups), their full groups (for Polish groups) and the amenable subalgebras of von Neumann algebras associated with hyperbolic groups and lattices of Lie groups. This dissertation is composed of three parts.The first part is devoted to the study of sofic entropy of profinite actions. Sofic entropy is an invariant for actions of sofic groups defined by L. Bowen that generalize Kolmogorov's entropy. The definition of sofic entropy makes use of a fixed sofic approximation of the group. We will show that the sofic entropy of profinite actions does depend on the chosen sofic approximation for free groups and some lattices of Lie groups. The second part is based on a joint work with François Le Maître. The content of this part is based on a prepublication in which we generalize the notion of full group to probability measure preserving actions of Polish groups, and in particular, of locally compact groups. We define a Polish topology on these full groups and we study their basic topological properties, such as the topological rank and the density of aperiodic elements. The third part is based on a joint work with Rémi Boutonnet. The content of this part is based on two prepublications in which we try to understand when the von Neumann algebra of a maximal amenable subgroup of a countable group is itself maximal amenable. We solve the question for hyperbolic and relatively hyperbolic groups using techniques due to Popa. With different techniques, we will then present a dynamical criterion which allow us to answer the question for some amenable subgroups of lattices of Lie groups of higher rank
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This dissertation is about measured group theory, sofic entropy and operator algebras. More precisely, we will study actions of groups on probability spaces, some fundamental properties of their sofic entropy (for countable groups), their full groups (for Polish groups) and the amenable subalgebras of von Neumann algebras associated with hyperbolic groups and lattices of Lie groups. This dissertation is composed of three parts.The first part is devoted to the study of sofic entropy of profinite actions. Sofic entropy is an invariant for actions of sofic groups defined by L. Bowen that generalize Kolmogorov's entropy. The definition of sofic entropy makes use of a fixed sofic approximation of the group. We will show that the sofic entropy of profinite actions does depend on the chosen sofic approximation for free groups and some lattices of Lie groups. The second part is based on a joint work with François Le Maître. The content of this part is based on a prepublication in which we generalize the notion of full group to probability measure preserving actions of Polish groups, and in particular, of locally compact groups. We define a Polish topology on these full groups and we study their basic topological properties, such as the topological rank and the density of aperiodic elements. The third part is based on a joint work with Rémi Boutonnet. The content of this part is based on two prepublications in which we try to understand when the von Neumann algebra of a maximal amenable subgroup of a countable group is itself maximal amenable. We solve the question for hyperbolic and relatively hyperbolic groups using techniques due to Popa. With different techniques, we will then present a dynamical criterion which allow us to answer the question for some amenable subgroups of lattices of Lie groups of higher rank
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Brown, Nathanial P. (Nathanial Patrick) 1972 Author
 American Mathematical Society
 Houdayer, Cyril (1980....). Opponent
 École Doctorale d'Informatique et Mathématiques (Lyon)
 Tsankov, Todor Opponent
 Carderi, Alessandro (1987....). Author
 Bekka, Bachir Opponent
 Unité de Mathématiques Pures et Appliquées (Lyon)
 Abert, Miklós
 École normale supérieure de Lyon Degree grantor
Useful Links
Associated Subjects
Covers
Alternative Names
Narutaka Ozawa Japanese mathematician
Narutaka Ozawa mathématicien japonais
小沢登高
Languages