相关论文: Behavior of Kreiss bounded $C_0$-semigroups on a H…

For a given $C_0$-semigroup $(T(t))_{t\geq 0}$ we consider Staffans-Weiss perturbations $(B,C)$ of its generator as studied in [1] and investigate the robustness of asymptotic properties of the perturbed $C_0$-semigroup $(T_{BC}(t))_{t\geq…

We present a short elementary proof of the Gearhart-Pr\"uss theorem for bounded $C_0$-semigroups on Hilbert spaces.

We analyse $C_0$-semigroups of contractive operators on real-valued $L^p$-spaces for $p \not= 2$ and on other classes of non-Hilbert spaces. We show that, under some regularity assumptions on the semigroup, the geometry of the unit ball of…

We reveal new aspects of the structure of Hilbert space $C_0$-semigroups $\mathcal T = (T(t))_{t\ge 0}$ similar to semigroups of contractions. In particular, we prove that $\mathcal T$ is similar to a semigroup of contractions if and only…

Motivated by B. Tsirelson's construction of $E_0$-semigroups of type III, we investigate a $C_0$-semigroup acting on the space of square integrable functions of the half line whose difference from the shift semigroup is a Hilbert-Schmidt…

We investigate rates of decay for $C_0$-semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains the best possible estimate on the rate of decay, that is to…

We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times…

In the context of a theorem of Richter, we establish a similarity between $C_0$-semigroups of analytic 2-isometries $\{T(t)\}_{t\geq0}$ acting on a Hilbert space $\mathcal H$ and the multiplication operator semigroup $\{M_{\phi_t}\}_{t\geq…

The well-known Batty's theorem states that if a $C_0$-semigroup $T(t)$ is bounded and the spectrum of the generator $A$ is contained in the open left-half plane of $\mathbb{C}$, then $\|T(t)A^{-1}\|$ tends to $0$. This can be thought of as…

Let $\{T(t)\}_{t\ge 0}$ be a $C_0$-semigroup on a separable Hilbert space $H$. We characterize that $T(t)$ is an $m$-isometry for every $t$ in terms that the mapping $t\in \Bbb R^+ \rightarrow \|T(t)x\|^2$ is a polynomial of degree less…

We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term "tight". These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the "tight…

The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual…

An interesting result by T. Kato and A. Pazy says that a contractive semigroup (T(t)) on a uniformly convex space X is holomorphic iff limsup_{t \downarrow 0} ||T(t)-Id|| < 2. We study extensions of this result which are valid on arbitrary…

Let H be a separable Hilbert space. Given two strongly commuting CP_0-semigroups $\phi$ and $\theta$ on B(H), there is a Hilbert space K containing H and two (strongly) commuting E_0-semigroups $\alpha$ and $\beta$ such that $\phi_s \circ…

We stretch the spectral bound equal growth bound condition along with a generalized Lyapunov stability theorem, known to hold for $C_0$-semigroups of normal operators on complex Hilbert spaces, to $C_0$-semigroups of scalar type spectral…

Let $(\phi_t)$ be a holomorphic semigroup of the unit disc (i.e., the flow of a semicomplete holomorphic vector field) without fixed points in the unit disc and let $\Omega$ be the starlike at infinity domain image of the Koenigs function…

We study decay rates for bounded $C_0$-semigroups from the perspective of $L^p$-infinite-time admissibility and related resolvent estimates. In the Hilbert space setting, polynomial decay of semigroup orbits is characterized by the…

A unitary representation of a, possibly infinite dimensional, Lie group G is called semi-bounded if the corresponding operators id\pi(x) from the derived representations are uniformly bounded from above on some non-empty open subset of the…

We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is based upon unbounded linear perturbations…

Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G. We show that there exist $\alpha_{1},\alpha_{2}\in\mathbb{R}, \beta\in\frac{1}{2}\mathbb{Z}$, and $l\in\mathbb{N}$ such that…