Smooth Homogeneous Structures in Operator Theory

 TOPOLOGICAL LIE ALGEBRAS
Fundamentals
Universal enveloping algebras
The Baker-Campbell-Hausdor series
Convergence of the Baker-Campbell-Hausdor series
Notes
LIE GROUPS AND THEIR LIE ALGEBRAS
Definition of Lie groups
The Lie algebra of a Lie group
Logarithmic derivatives
The exponential map
Special features of Banach-Lie groups
Notes
ENLARGIBILITY
Integrating Lie algebra homomorphisms
Topological properties of certain Lie groups
Enlargible Lie algebras
Notes
Smooth Homogeneous Spaces
Basic facts on smooth homogeneous spaces
Symplectic homogeneous spaces
Some homogeneous spaces related to operator algebras
Notes
QUASIMULTIPLICATIVE MAPS
Supports, convolution, and quasimultiplicativity
Separate parts of supports
Hermitian maps
Notes
COMPLEX STRUCTURES ON HOMOGENEOUS SPACES
General results
Pseudo-Kähler manifolds
Flag manifolds in Banach algebras
Notes
EQUIVARIANT MONOTONE OPERATORS
Definition of equivariant monotone operators
H*-algebras and L*-algebras
Equivariant monotone operators as reproducing kernels
H*-ideals of H*-algebras
Elementary properties of H*-ideals
Notes
L*-IDEALS AND EQUIVARIANT MONOTONE OPERATORS
From ideals to operators
From operators to ideals
Parameterizing L*-ideals
Representations of automorphism groups
Applications to enlargibility
Notes
HOMOGENEOUS SPACES OF PSEUDO-RESTRICTED GROUPS
Pseudo-restricted algebras and groups
Complex polarizations
Kähler polarizations
Admissible pairs of operator ideals
Some Kähler homogeneous spaces
Notes
APPENDICES
Differential Calculus and Smooth Manifolds
Basic Differential Equations of Lie Theory
Topological Groups

References
Index