Asymptotic behaviour of semigroups of nonnegative operators on a Banach lattice

Jolanta Socała

Displaying similar documents to “Asymptotic behaviour of semigroups of nonnegative operators on a Banach lattice”

C₀-semigroups generated by second order differential operators

Gabriela Raluca Mocanu (2016)

Annales Polonici Mathematici

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Let $W (u) (x) = 1 / 2 x^{a} {(1 - x)}^{b} u^{''} (x)$ with a,b ≥ 2. We consider the C₀-semigroups generated by this operator on the spaces of continuous functions, respectively square integrable functions. The connection between these semigroups together with suitable approximation processes is studied. Also, some qualitative and quantitative properties are derived.

Compactness properties of Feller semigroups

G. Metafune, D. Pallara, M. Wacker (2002)

Studia Mathematica

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We study the compactness of Feller semigroups generated by second order elliptic partial differential operators with unbounded coefficients in spaces of continuous functions in $ℝ^{N}$ .

Asymptotic behaviour of the iterates of nonnegative operators on a Banach lattice

Jolanta Socała (1998)

Annales Polonici Mathematici

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Asymptotic convergence theorems for nonnegative operators on Banach lattices, on $L^{\infty}$ , on C(X) and on $L^{p} (1 \leq p < \infty)$ are proved. The general results are applied to a class of integral operators on L¹.

Classes of distribution semigroups

Peer Christian Kunstmann, Modrag Mijatović, Stevan Pilipović (2008)

Studia Mathematica

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We introduce various classes of distribution semigroups distinguished by their behavior at the origin. We relate them to quasi-distribution semigroups and integrated semigroups. A class of such semigroups, called strong distribution semigroups, is characterized through the value at the origin in the sense of Łojasiewicz. It contains smooth distribution semigroups as a subclass. Moreover, the analysis of the behavior at the origin involves intrinsic structural results for semigroups....

On the positivity of semigroups of operators

Roland Lemmert, Peter Volkmann (1998)

Commentationes Mathematicae Universitatis Carolinae

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In a Banach space $E$ , let $U (t)$ $(t > 0)$ be a $C_{0}$ -semigroup with generating operator $A$ . For a cone $K \subseteq E$ with non-empty interior we show: $(☆)$ $U (t) [K] \subseteq K$ $(t > 0)$ holds if and only if $A$ is quasimonotone increasing with respect to $K$ . On the other hand, if $A$ is not continuous, then there exists a regular cone $K \subseteq E$ such that $A$ is quasimonotone increasing, but $(☆)$ does not hold.

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.

Envelope functions and asymptotic structures in Banach spaces

Bünyamin Sarı (2004)

Studia Mathematica

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We introduce a notion of disjoint envelope functions to study asymptotic structures of Banach spaces. The main result gives a new characterization of asymptotic- $ℓ_{p}$ spaces in terms of the $ℓ_{p}$ -behavior of “disjoint-permissible” vectors of constant coefficients. Applying this result to Tirilman spaces we obtain a negative solution to a conjecture of Casazza and Shura. Further investigation of the disjoint envelopes leads to a finite-representability result in the spirit of the Maurey-Pisier...

On semigroups of $σ$ -endomorphisms

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Semiflows and semigroups

Edoardo Vesentini (1996)

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

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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.

The asymptotic behaviour of the counting functions of Ω-sets in arithmetical semigroups

Maciej Radziejewski (2014)

Acta Arithmetica

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We consider an axiomatically-defined class of arithmetical semigroups that we call simple L-semigroups. This class includes all generalized Hilbert semigroups, in particular the semigroup of non-zero integers in any algebraic number field. We show, for all positive integers k, that the counting function of the set of elements with at most k distinct factorization lengths in such a semigroup has oscillations of logarithmic frequency and size $\sqrt x {(l o g x)}^{- M}$ for some M>0. More generally, we show...

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...