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Cover: 9783111597911 | Algebras of Unbounded Operators | Aleksey Ber (u. a.) | Taschenbuch
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Algebras of Unbounded Operators
Algebraic and Topological Aspects of Murray-von Neumann Algebras
Taschenbuch von Aleksey Ber (u. a.)
Sprache: Englisch

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Beschreibung
Derivations on von Neumann algebras are well understood and are always inner, meaning that they act as commutators with a fixed element from the algebra itself. The purpose of this book is to provide a complete description of derivations on algebras of operators affiliated with a von Neumann algebra. The book is designed to serve as an introductory graduate level to various measurable operators affiliated with a von Neumann algebras and their properties. These classes of operators form their respective algebras and the problem of describing derivations on these algebras was raised by Ayupov, and later by Kadison and Liu. A principal aim of the book is to fully resolve the Ayupov-Kadison-Liu problem by proving a necessary and sufficient condition of the existence of non-inner derivation of algebras of measurable operators. It turns out that only for a finite type I von Neumann algebra M may there exist a non-inner derivation on the algebra of operators affiliated with M. In particular, it is established that the classical derivation d/dt of functions of real variables can be extended up to a derivation on the algebra of all measurable functions. This resolves a long-standing problem in classical analysis.
Derivations on von Neumann algebras are well understood and are always inner, meaning that they act as commutators with a fixed element from the algebra itself. The purpose of this book is to provide a complete description of derivations on algebras of operators affiliated with a von Neumann algebra. The book is designed to serve as an introductory graduate level to various measurable operators affiliated with a von Neumann algebras and their properties. These classes of operators form their respective algebras and the problem of describing derivations on these algebras was raised by Ayupov, and later by Kadison and Liu. A principal aim of the book is to fully resolve the Ayupov-Kadison-Liu problem by proving a necessary and sufficient condition of the existence of non-inner derivation of algebras of measurable operators. It turns out that only for a finite type I von Neumann algebra M may there exist a non-inner derivation on the algebra of operators affiliated with M. In particular, it is established that the classical derivation d/dt of functions of real variables can be extended up to a derivation on the algebra of all measurable functions. This resolves a long-standing problem in classical analysis.
Details
Erscheinungsjahr: 2025
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: XII
408 S.
ISBN-13: 9783111597911
ISBN-10: 3111597911
Sprache: Englisch
Ausstattung / Beilage: Großformatiges Paperback. Klappenbroschur
Autor: Ber, Aleksey
Chilin, Vladimir
Levitina, Galina
Sukochev, Fedor
Zanin, Dmitriy
Hersteller: De Gruyter
Verantwortliche Person für die EU: Walter de Gruyter GmbH, De Gruyter GmbH, Genthiner Str. 13, D-10785 Berlin, productsafety@degruyterbrill.com
Von/Mit: Aleksey Ber (u. a.)
Erscheinungsdatum: 03.03.2025
Gewicht: 0,682 kg
Artikel-ID: 131614105
Details
Erscheinungsjahr: 2025
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: XII
408 S.
ISBN-13: 9783111597911
ISBN-10: 3111597911
Sprache: Englisch
Ausstattung / Beilage: Großformatiges Paperback. Klappenbroschur
Autor: Ber, Aleksey
Chilin, Vladimir
Levitina, Galina
Sukochev, Fedor
Zanin, Dmitriy
Hersteller: De Gruyter
Verantwortliche Person für die EU: Walter de Gruyter GmbH, De Gruyter GmbH, Genthiner Str. 13, D-10785 Berlin, productsafety@degruyterbrill.com
Von/Mit: Aleksey Ber (u. a.)
Erscheinungsdatum: 03.03.2025
Gewicht: 0,682 kg
Artikel-ID: 131614105
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