We prove the following. Let T = fT(t)g t0 be a bounded C 0-semigroup on a Banach space X and A its innnitesimal generator. Then <(A) < 0 if and only if sup t>0 jj t Z 0 e iii T()ddjj < 1; 8 2 R; 8x 2 X: In particular we obtain that a strongly continuous and exponentially bounded family of bounded linear operators U on X is uniformly exponentially stable if and only if the spectrum of the innnit...

In this note, we answer a question raised by Johnson and Schechtman [7], about the hypercontractive semigroup on {−1, 1}. More generally, we prove the theorem below. 2000 Math. Subject Classification: Primary 47D20. Seconday 47L20. In this note, we answer a question raised by Johnson and Schechtman [7]. We refer to their paper for motivation and background. In addition, we refer the reader to [...

That is, W0 is the set of all finite products of the generators, allowing repetitions. Let W signify the larger multiplicative semigroup generated by W0 together with {1/2}. We call W the wild semigroup and W0 the Wooley semigroup. The question we consider is: Which integers belong to these semigroups? The sets of integer elements W(Z) := W ∩ Z and W0(Z) := W0 ∩ Z themselves form multiplicative...

We consider the semigroup on L 1 (IR n) deened by the nonlinear transport equation for the scalar s @ t s + div(f(s) u) = 0 in (0; 1)I R n for given velocity eld u. We show that this nonlinear semigroup is HH older continuous for t > 0 in the uniform operator topology, provided the graph of f has no linear segments. This continuity property | which expresses a regularizing eeect of the nonlinea...

We show that the existence of a nontrivial bounded uniformly continuous (BUC) complete trajectory for a C0-semigroup TA(t) generated by an operator A in a Banach space X is equivalent to the existence of a solution Π = δ0 to the homogenous operator equation ΠS|M = AΠ. Here S|M generates the shift C0-group TS(t)|M in a closed translation-invariant subspaceM of BUC(R, X), and δ0 is the point eval...

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).

Let Z be a Banach lattice endowed with positive cone C and an order-continuous norm j.j . Let G be a left-amenable semigroup of positive linear endomorphisms of Z . Then the positive fixed points Co of Z under G form a lattice cone, and their linear span Z0 is a Banach lattice under an order-continuous norm ||.||0 which agrees with |.| on Co. A counterexample shows that under the given conditio...

3 The paper gives a short account of some basic properties of Dirichlet-to-Neumann operators Λ γ,∂Ω including the corresponding semigroups motivated by the Lapla-cian transport in anisotropic media (γ = I) and by elliptic systems with dynam-ical boundary conditions. For illustration of these notions and the properties we use the explicitly constructed Lax semigroups. We demonstrate that for a g...

For a differential equation of the form $u'(t) + Au(t) = f(t), t \in (0,\infty)$, where $A$ is infinitesimal generator bounded analytic $C_{0}$-semigroup linear operators in Banach space $\mathfrak{B}, \ f(t)$ $\mathfrak{B}$-valued polynomial, behavior preassigned points solutions Cauchy problem $u(0) u_{0} \mathfrak{B}$ depending on $f(t)$ investigated.

In this paper, we prove the following theorem: Let {T (t) : t ≥ 0} be a one-parameter continuous semigroup of mappings on a subset C of a Banach space E. The set of fixed points of T (t) is denoted by F (