Functional Analysis And Semi-Groups

  title={Functional Analysis And Semi-Groups},
  author={Einar Hille},
Part One. Functional Analysis: Abstract spaces Linear transformations Vector-valued functions Banach algebras General properties Analysis in a Banach algebra Laplace integrals and binomial series Part Two. Basic Properties of Semi-Groups: Subadditive functions Semi-modules Addition theorem in a Banach algebra Semi-groups in the strong topology Generator and resolvent Generation of semi-groups Part Three. Advanced Analytical Theory of Semi-Groups: Perturbation theory Adjoint theory Operational… Expand
On contraction semi-groups and (di)-operators
Lumet and Phillips [5] have studied semi-groups of linear contraction operators in a Banach space by virtue of the notation of semi-inner product introduced by Lumer. The infinitesimal generator ofExpand
Spectral and ergodic properties of the analytic generators
Abstract In this paper similarity situations between one-parameter groups of operators are characterized in terms of analytic generators and spectral subspaces, and ergodic properties ofExpand
Semi-Groups of Contraction Operators
The theory of semi-groups of linear operators had its origin in Stone's theorem on groups of unitary operators acting in a Hilbert space (1932). Stone's theorem was motivated by the time dependentExpand
Composition operators on vector-valued analytic function spaces: a survey
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values inExpand
Induced Banach representations of Banach algebras and locally compact groups
respectively (the Frobenius reciprocity theorem can be considered to be the statement of these equivalences). Th e purpose of th is paper is to investigate the extent to which the situation describedExpand
It is well known that a complex-valued function , analytic on some open set ft, extends to any commutative Banach algebra B so that the action of 0 on B commutes with the action of the GelfandExpand
Slice regular semigroups
In this paper we introduce the notion of slice regular right linear semigroup in a quaternionic Banach space. It is an operatorial function which is slice regular (a noncommutative counterpart ofExpand
Rigidity and Parametric Embedding of Semi-complete Vector Fields on the Unit Disk
This manuscript contains recent results on generation theory of semigroups of holomorphic mappings with applications to geometric function theory as well as new results which could define some newExpand
Categories of unitary representations of Banach-Lie supergroups and restriction functors
We prove that the categories of smooth and analytic unitary representations of Banach--Lie supergroups are well-behaved under restriction functors, in the sense that the restriction of aExpand
Spectral invariance of Besov-Bessel subalgebras
Using principles of the theory of smoothness spaces, we give systematic constructions of scales of inverse-closed subalgebras of a given Banach algebra with the action of a d-parameter automorphismExpand