Journal ArticleDOI
The Similarity Problem for Bounded Analytic Semigroups on Hilbert Space
TLDR
In this paper, the authors established conditions under which (Tt)t≥0 is similar to a contraction semigroup, i.e., there exists an isomorphism S E B (H) such that (S-1 Tt S)t ≥ 0 is a contraction semiigroup.Abstract:
)t≥0 on a Hilbert space H, we establish conditions under which (Tt)t≥0 is similar to a contraction semigroup, i.e., there exists an isomorphism S E B (H) such that (S-1 Tt S)t≥0 is a contraction semigroup. In the case when the generator -A of (Tt)t≥0 is one-to-one, we obtain that (Tt)t≥0 is similar to a contraction semigroup if and only if A admits bounded imaginary powers. This characterizes one-to-one operators of type strictly less than π/2 on H which belong to BIP (H).read more
Citations
More filters
Book
The Functional Calculus for Sectorial Operators
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.
Book ChapterDOI
Chapter 1 Semigroups and evolution equations: Functional calculus, regularity and kernel estimates
TL;DR: A survey on recent developments of the theory of one-parameter semigroups and evolution equations with special emphasis on functional calculus and kernel estimates can be found in this paper, where the main application is elliptic operators with various boundary conditions.
Journal ArticleDOI
H[∞]functional calculus and square functions on noncommutative L[p]-spaces
TL;DR: In this article, sectorial operators and semigroups acting on noncommutative L-spaces are investigated and their connection with H∞ functional calculus is discussed. But the authors mainly focus on diffusion semigroup, that is, semiggroups (Tt)t ≥ 0 of normal selfadjoint operators on a seminite von Neumann algebra (M, τ) such that Tt : Lp(M) → Lp (M) is a contraction for any p ≥ 1 and any t ≥ 0.
Journal ArticleDOI
Transition Semigroups of Banach Space Valued Ornstein-Uhlenbeck Processes
TL;DR: In this paper, the transition semigroup of the solution to a stochastic evolution equation is investigated, where A is the generator of a C 0-semigroup S on a separable real Banach space E and W is cylindrical white noise with values in a real Hilbert space H which is continuously embedded in E. Various properties of these semigroups, such as the strong Feller property, the spectral gap property, and analyticity, are characterized in terms of the behaviour of S in H.