Introductory Functional Analysis with Applications
Published on 1991
The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.
Introductory Functional Analysis with Applications
The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.
Lectures on von Neumann Algebras
Published on 2019
Written in lucid language, this valuable text discusses fundamental concepts of von Neumann algebras including bounded linear operators in Hilbert spaces, finite von Neumann algebras, linear forms on algebra of operators, geometry of projections and classification of von Neumann algebras in an easy to understand manner. The revised text covers new material including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras with a cyclic and separating vector. Pedagogical features including solved problems and exercises are interspersed throughout the book.
- New topics including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras are discussed in detail
- Covers the theory of standard von Neumann algebras, first in the classical semi-finite case, then in the case where there is a cyclic and separating vector, and finally in general cases
- Pedagogical features including solved problems and exercises are interspersed throughout the book
Lectures on von Neumann Algebras
Written in lucid language, this valuable text discusses fundamental concepts of von Neumann algebras including bounded linear operators in Hilbert spaces, finite von Neumann algebras, linear forms on algebra of operators, geometry of projections and classification of von Neumann algebras in an easy to understand manner. The revised text covers new material including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras with a cyclic and separating vector. Pedagogical features including solved problems and exercises are interspersed throughout the book.
- New topics including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras are discussed in detail
- Covers the theory of standard von Neumann algebras, first in the classical semi-finite case, then in the case where there is a cyclic and separating vector, and finally in general cases
- Pedagogical features including solved problems and exercises are interspersed throughout the book
Locally Convex Spaces
Published on 2016
For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis.
While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.
Locally Convex Spaces
For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis.
While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.
Noncommutative Integration and Operator Theory
Published on 2024
The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.
Noncommutative Integration and Operator Theory
The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.
Real and Functional Analysis
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis.This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis.This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis.
Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references.
The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
Real and Functional Analysis
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis.This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis.This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis.
Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references.
The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
Semi-Simple Groups and Symmetric Spaces
Up to minor changes, these are the Notes of a series of lectures given at the Tata Institute of Fundamental Research, Mumbai. They cover some basic material on affine connections, locally or globally Riemannian and Hermitian symmetric spaces. A last chapter proves the basic theorems on maximal compact subgroups of Lie groups with finitely many connected components. Familiarity with differential manifolds and the elementary theory of Lie groups and Lie algebras is assumed.
Semi-Simple Groups and Symmetric Spaces
Up to minor changes, these are the Notes of a series of lectures given at the Tata Institute of Fundamental Research, Mumbai. They cover some basic material on affine connections, locally or globally Riemannian and Hermitian symmetric spaces. A last chapter proves the basic theorems on maximal compact subgroups of Lie groups with finitely many connected components. Familiarity with differential manifolds and the elementary theory of Lie groups and Lie algebras is assumed.
