Smooth Homogeneous Structures in Operator Theory (Hardcover)

TOPOLOGICAL LIE ALGEBRASFundamentalsUniversal enveloping algebras The Baker-Campbell-Hausdor seriesConvergence of the Baker-Campbell-Hausdor seriesNotes LIE GROUPS AND THEIR LIE ALGEBRAS Definition of Lie groupsThe Lie algebra of a Lie groupLogarithmic derivativesThe exponential map Special features of Banach-Lie groupsNotes ENLARGIBILITY Integrating Lie algebra homomorphisms Topological properties of certain Lie groups Enlargible Lie algebrasNotes Smooth Homogeneous Spaces Basic facts on smooth homogeneous spaces Symplectic homogeneous spaces Some homogeneous spaces related to operator algebrasNotes QUASIMULTIPLICATIVE MAPS Supports, convolution, and quasimultiplicativitySeparate parts of supportsHermitian mapsNotes COMPLEX STRUCTURES ON HOMOGENEOUS SPACES General results Pseudo-Kahler manifolds Flag manifolds in Banach algebrasNotes EQUIVARIANT MONOTONE OPERATORS Definition of equivariant monotone operatorsH*-algebras and L*-algebras Equivariant monotone operators as reproducing kernelsH*-ideals of H*-algebras Elementary properties of H*-idealsNotes L*-IDEALS AND EQUIVARIANT MONOTONE OPERATORS From ideals to operators From operators to ideals Parameterizing L*-ideals Representations of automorphism groupsApplications to enlargibility Notes HOMOGENEOUS SPACES OF PSEUDO-RESTRICTED GROUPS Pseudo-restricted algebras and groupsComplex polarizations Kahler polarizationsAdmissible pairs of operator idealsSome Kahler homogeneous spacesNotes APPENDICESDifferential Calculus and Smooth Manifolds Basic Differential Equations of Lie Theory Topological Groups References Index