Ebook: Introduction to the Theory of Banach Representations of Groups

1 — Elements of Spectral Theory.- 1. Integration of vector-valued functions.- 2. Linear operators in Banach space.- 3. Spectrum and resolvent of linear operators.- 4. Invariant subspaces.- 5. Commutative Banach algebras.- 2 — Topological Groups and Semigroups.- 1. Topological groups.- 2. Topological semigroups.- 3. Invariant measures and means.- 3 — Elements of General Representation Theory.- 1. Actions and representations.- 2. Decomposition of representations.- 3. Finite dimensional representations.- 4. The representation spectrum of an Abelian semigroup.- 4 — Representations of Compact Semigroups.- 1. Harmonic analysis on compact groups.- 2. Banach representations of compact groups and semigroups.- 3. Almost periodic representations and functions.- 4. Nonnegative a.p. representations.- 5 — Representations of Locally Compact Abelian Groups.- 1. Elements of harmonic analysis.- 2. Representations with separable spectrum.- References.- Books.- Journal Articles.