Embedding operators into strongly continuous semigroups

TL;DR: For the weak operator topology, Eisner et al. as mentioned in this paper showed that the set of unitary operators on a separable in-dimensional Hilbert space is residual in all contractions.

TL;DR: In this article, the authors studied the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity and showed that a "typical" contraction $T$ contains the unit circle times the identity operator in the strong limit set of its powers, while $T^{n_j}$ converges weakly to zero along a sequence with density one.

TL;DR: In this paper, the authors studied the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies.

TL;DR: In this article, the authors studied the closely related questions of embedding discrete Markov chains into continuous ones, which is a famous open problem in probability theory and has many applications.

TL;DR: In this article, the structure of operators of Class C 0.1 is discussed.Contractions and their Dilations, Geometrical and Spectral Properties of Dilations and Operator-Valued Analytic Functions are discussed.

TL;DR: In this article, an introductory text in functional analysis aimed at the graduate student with a firm background in integration and measure theory is presented, which helps the student to develop an intuitive feel for the subject.

TL;DR: In this article, the basic theory of sectorial operators is developed along the lines of the abstract framework of Chapter 1 Fundamental properties like the composition rule are proved and a panorama of functional calculi is developed.