Displaying similar documents to “On a vector-valued local ergodic theorem in L ∞ ”

Vector-valued ergodic theorems for multiparameter additive processes

Ryotaro Sato (1999)

Colloquium Mathematicae

Similarity:

Let X be a reflexive Banach space and (Ω,Σ,μ) be a σ-finite measure space. Let d ≥ 1 be an integer and T=T(u):u=( u 1 , ... , u d ) , u i ≥ 0, 1 ≤ i ≤ d be a strongly measurable d-parameter semigroup of linear contractions on L 1 ((Ω,Σ,μ);X). We assume that to each T(u) there corresponds a positive linear contraction P(u) defined on L 1 ((Ω,Σ,μ);ℝ) with the property that ∥ T(u)f(ω)∥ ≤ P(u)∥f(·)∥(ω) almost everywhere on Ω for all f ∈ L 1 ((Ω,Σ,μ);X). We then prove stochastic and pointwise ergodic theorems...

Is A - 1 an infinitesimal generator?

Hans Zwart (2007)

Banach Center Publications

Similarity:

In this paper we study the question whether A - 1 is the infinitesimal generator of a bounded C₀-semigroup if A generates a bounded C₀-semigroup. If the semigroup generated by A is analytic and sectorially bounded, then the same holds for the semigroup generated by A - 1 . However, we construct a contraction semigroup with growth bound minus infinity for which A - 1 does not generate a bounded semigroup. Using this example we construct an infinitesimal generator of a bounded semigroup for which its...

A general differentiation theorem for multiparameter additive processes

Ryotaro Sato (2002)

Colloquium Mathematicae

Similarity:

Let ( L , | | · | | L ) be a Banach lattice of equivalence classes of real-valued measurable functions on a σ-finite measure space and T = T ( u ) : u = ( u ₁ , . . . , u d ) , u i > 0 , 1 ≤ i ≤ d be a strongly continuous locally bounded d-dimensional semigroup of positive linear operators on L. Under suitable conditions on the Banach lattice L we prove a general differentiation theorem for locally bounded d-dimensional processes in L which are additive with respect to the semigroup T.

On ergodicity for operators with bounded resolvent in Banach spaces

Kirsti Mattila (2011)

Studia Mathematica

Similarity:

We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that | | α ( α - A ) - 1 | | is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the...

Semiflows and semigroups

Edoardo Vesentini (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Given a compact Hausdorff space K and a strongly continuous semigroup T of linear isometries of the Banach space of all complex-valued, continuous functions on K , the semiflow induced by T on K is investigated. In the particular case in which K is a compact, connected, differentiable manifold, a class of semigroups T preserving the differentiable structure of K is characterized.

On the theory of remediability

Hassan Emamirad (2003)

Banach Center Publications

Similarity:

Suppose G ₁ ( t ) t ≥ 0 and G ₂ ( t ) t ≥ 0 are two families of semigroups on a Banach space X (not necessarily of class C₀) such that for some initial datum u₀, G₁(t)u₀ tends towards an undesirable state u*. After remedying by means of an operator ρ we continue the evolution of the state by applying G₂(t) and after time 2t we retrieve a prosperous state u given by u = G₂(t)ρG₁(t)u₀. Here we are concerned with various properties of the semigroup (t): ρ → G₂(t)ρG₁(t). We define (X) to be the space of remedial operators...

Vector-valued ergodic theorems for multiparameter Additive processes II

Ryotaro Sato (2003)

Colloquium Mathematicae

Similarity:

Previously we obtained stochastic and pointwise ergodic theorems for a continuous d-parameter additive process F in L₁((Ω,Σ,μ);X), where X is a reflexive Banach space, under the condition that F is bounded. In this paper we improve the previous results by considering the weaker condition that the function W ( · ) = e s s s u p | | F ( I ) ( · ) | | : I ⊂ [ 0 , 1 ) d is integrable on Ω.

On semigroups with an infinitesimal operator

Jolanta Olko (2005)

Annales Polonici Mathematici

Similarity:

Let F t : t ≥ 0 be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small t every linear selection of F t is invertible and there exists an exponential semigroup f t : t ≥ 0 of linear continuous selections f t of F t .

The one-sided ergodic Hilbert transform in Banach spaces

Guy Cohen, Christophe Cuny, Michael Lin (2010)

Studia Mathematica

Similarity:

Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform l i m n ∑ k = 1 n ( T k x ) / k . We prove that weak and strong convergence are equivalent, and in a reflexive space also s u p n | | ∑ k = 1 n ( T k x ) / k | | < ∞ is equivalent to the convergence. We also show that - ∑ k = 1 ∞ ( T k ) / k (which converges on (I-T)X) is precisely the infinitesimal generator of the semigroup ( I - T ) | ( I - T ) X ¯ r .

Locally adequate semigroup algebras

Yingdan Ji, Yanfeng Luo (2016)

Open Mathematics

Similarity:

We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant [...] 0-J* 0 - 𝒥 * -simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] ℛ* ℛ * -classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we...