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Smooth Homogeneous Structures in Operator Theory

Af: Daniel Beltita Engelsk Paperback
SPAR
kr 103

Smooth Homogeneous Structures in Operator Theory

Af: Daniel Beltita Engelsk Paperback
Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras. Smooth Homogeneous Structures in Operator Theory builds the background needed to understand this circle of ideas and reports on recent developments in this fruitful field of research.

Requiring only a moderate familiarity with functional analysis and general topology, the author begins with an introduction to infinite dimensional Lie theory with emphasis on the relationship between Lie groups and Lie algebras. A detailed examination of smooth homogeneous spaces follows. This study is illustrated by familiar examples from operator theory and develops methods that allow endowing such spaces with structures of complex manifolds. The final section of the book explores equivariant monotone operators and Kähler structures. It examines certain symmetry properties of abstract reproducing kernels and arrives at a very general version of the construction of restricted Grassmann manifolds from the theory of loop groups.

The author provides complete arguments for nearly every result. An extensive list of references and bibliographic notes provide a clear picture of the applicability of geometric methods in functional analysis, and the open questions presented throughout the text highlight interesting new research opportunities.

Daniel Beltitâ is a Principal Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Bucharest, Romania.
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Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras. Smooth Homogeneous Structures in Operator Theory builds the background needed to understand this circle of ideas and reports on recent developments in this fruitful field of research.

Requiring only a moderate familiarity with functional analysis and general topology, the author begins with an introduction to infinite dimensional Lie theory with emphasis on the relationship between Lie groups and Lie algebras. A detailed examination of smooth homogeneous spaces follows. This study is illustrated by familiar examples from operator theory and develops methods that allow endowing such spaces with structures of complex manifolds. The final section of the book explores equivariant monotone operators and Kähler structures. It examines certain symmetry properties of abstract reproducing kernels and arrives at a very general version of the construction of restricted Grassmann manifolds from the theory of loop groups.

The author provides complete arguments for nearly every result. An extensive list of references and bibliographic notes provide a clear picture of the applicability of geometric methods in functional analysis, and the open questions presented throughout the text highlight interesting new research opportunities.

Daniel Beltitâ is a Principal Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Bucharest, Romania.
Produktdetaljer
Sprog: Engelsk
Sider: 318
ISBN-13: 9780367391898
Indbinding: Paperback
Udgave:
ISBN-10: 0367391899
Kategori: Algebra
Udg. Dato: 23 okt 2019
Længde: 0mm
Bredde: 234mm
Højde: 156mm
Forlag: Taylor & Francis Ltd
Oplagsdato: 23 okt 2019
Forfatter(e): Daniel Beltita
Forfatter(e) Daniel Beltita


Kategori Algebra


Sprog Engelsk


Indbinding Paperback


Sider 318


Udgave


Længde 0mm


Bredde 234mm


Højde 156mm


Udg. Dato 23 okt 2019


Oplagsdato 23 okt 2019

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