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 Kahler
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 Beltita is a Principal Researcher at the
Institute of Mathematics "Simion Stoilow" of the Romanian Academy,
Bucharest, Romania.
General
Imprint: |
Crc Press
|
Country of origin: |
United Kingdom |
Series: |
Monographs and Surveys in Pure and Applied Mathematics |
Release date: |
October 2019 |
First published: |
2006 |
Authors: |
Daniel Belti t a
|
Dimensions: |
234 x 156mm (L x W) |
Format: |
Paperback
|
Pages: |
318 |
ISBN-13: |
978-0-367-39189-8 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
0-367-39189-9 |
Barcode: |
9780367391898 |
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