Semiflows and semigroups

Edoardo Vesentini

Displaying similar documents to “Semiflows and semigroups”

On the theory of remediability

Hassan Emamirad (2003)

Banach Center Publications

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Suppose ${G ₁ (t)}_{t \geq 0}$ and ${G ₂ (t)}_{t \geq 0}$ 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...

Is $A^{- 1}$ an infinitesimal generator?

Hans Zwart (2007)

Banach Center Publications

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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...

Linear modulus of a multidimensional semigroup of $L_{1}$ -contractions and a differentiation theorem

Dogan Çömez (1989)

Colloquium Mathematicae

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On a vector-valued local ergodic theorem in $L_{\infty}$

Ryotaro Sato (1999)

Studia Mathematica

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Let $T = T (u) : u \in ℝ_{d}^{+}$ be a strongly continuous d-dimensional semigroup of linear contractions on $L_{1} ((Ω, Σ, μ); X)$ , where (Ω,Σ,μ) is a σ-finite measure space and X is a reflexive Banach space. Since $L_{1} ((Ω, Σ, μ); X) * = L_{\infty} ((Ω, Σ, μ); X *)$ , the adjoint semigroup $T * = T * (u) : u \in ℝ_{d}^{+}$ becomes a weak*-continuous semigroup of linear contractions acting on $L_{\infty} ((Ω, Σ, μ); X *)$ . In this paper the local ergodic theorem is studied for the adjoint semigroup T*. Assuming that each T(u), $u \in ℝ_{d}^{+}$ , has a contraction majorant P(u) defined on $L_{1} ((Ω, Σ, μ); ℝ)$ , that is, P(u) is a positive linear contraction on $L_{1} ((Ω, Σ, μ); ℝ)$ such that $‖ T (u) f (ω) ‖ \leq P (u) ‖ f (\cdot) ‖ (ω)$ almost...

A general differentiation theorem for multiparameter additive processes

Ryotaro Sato (2002)

Colloquium Mathematicae

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Let $(L, | | \cdot | |_{L})$ be a Banach lattice of equivalence classes of real-valued measurable functions on a σ-finite measure space and $T = T (u) : u = (u ₁, . . ., u_{d}), u_{i} > 0, 1 \leq i \leq d$ 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.

Good and very good magnifiers

Marin Gutan (2000)

Bollettino dell'Unione Matematica Italiana

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Un elemento $a$ di un semigruppo $S$ è un elemento accrescitivo sinistro se la traslazione $λ_{a}$ di $S$ , associata all'elemento $a$ , è surgettiva e non è iniettiva (E. S. Ljapin, [13], § 5). Così, per ogni elemento accrescitivo sinistro $a$ , esiste un sottoinsieme proprio $M$ di $S$ tale che la restrizione a $M$ di $λ_{a}$ è biunivoca. Se $M$ è un sottosemigruppo (risp. un ideale destro) di $S$ , l'elemento accrescitivo sinistro $a$ viene detto buono (risp. molto buono) (F. Migliorini [15], [16], [17]). Utilizzando...

On ergodicity for operators with bounded resolvent in Banach spaces

Kirsti Mattila (2011)

Studia Mathematica

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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...

On a probabilistic problem on finite semigroups

Attila Nagy, Csaba Tóth (2023)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the following problem: how does the structure of a finite semigroup $S$ depend on the probability that two elements selected at random from $S$ , with replacement, define the same inner right translation of $S$ . We solve a subcase of this problem. As the main result of the paper, we show how to construct not necessarily finite medial semigroups in which the index of the kernel of the right regular representation equals two.

On semigroups with an infinitesimal operator

Jolanta Olko (2005)

Annales Polonici Mathematici

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Let $F^{t} : t \geq 0$ 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 $f^{t} : t \geq 0$ of linear continuous selections $f^{t}$ of $F^{t}$ .

Normal cryptogroups with an associate subgroup

Mario Petrich (2013)

Czechoslovak Mathematical Journal

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Let $S$ be a semigroup. For $a, x \in S$ such that $a = a x a$ , we say that $x$ is an associate of $a$ . A subgroup $G$ of $S$ which contains exactly one associate of each element of $S$ is called an associate subgroup of $S$ . It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup $S$ is a completely regular semigroup whose $ℋ$ -relation is a congruence and $S / ℋ$ is a normal band. Using the representation of $S$ as a strong semilattice of Rees matrix...

A $C^{*}$ -algebraic Schoenberg theorem

Ola Bratteli, Palle E. T. Jorgensen, Akitaka Kishimoto, Donald W. Robinson (1984)

Annales de l'institut Fourier

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Let $𝔄$ be a $C^{*}$ -algebra, $G$ a compact abelian group, $τ$ an action of $G$ by $*$ -automorphisms of $𝔄, 𝔄^{τ}$ the fixed point algebra of $τ$ and $𝔄_{F}$ the dense sub-algebra of $G$ -finite elements in $𝔄$ . Further let $H$ be a linear operator from $𝔄_{F}$ into $𝔄$ which commutes with $τ$ and vanishes on $𝔄^{τ}$ . We prove that $H$ is a complete dissipation if and only if $H$ is closable and its closure generates a $C_{0}$ -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative...