The maximal subsemigroups of the ideals of some semigroups of partial injections

Ilinka Dimitrova; Jörg Koppitz

Displaying similar documents to “The maximal subsemigroups of the ideals of some semigroups of partial injections”

Inverses of generators of nonanalytic semigroups

Ralph deLaubenfels (2009)

Studia Mathematica

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Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup ${e^{t A}}_{t \geq 0}$ . It is shown that $A^{- 1}$ generates an $O (1 + τ) A {(1 - A)}^{- 1}$ -regularized semigroup. Several equivalences for $A^{- 1}$ generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of ${e^{t A}}_{t \geq 0}$ , on subspaces, for $A^{- 1}$ generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate...

On semigroups of $σ$ -endomorphisms

Iwanik, Anzelm

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Analytic semigroups on vector valued noncommutative $L^{p}$ -spaces

Cédric Arhancet (2013)

Studia Mathematica

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We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ( ${(T \otimes I d_{E})}_{t \geq 0}$ on the vector valued noncommutative $L^{p}$ -space $L^{p} (M, E)$ . Moreover, we give applications to the $H^{\infty} (Σ_{θ})$ functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

A local Landau type inequality for semigroup orbits

Gerd Herzog, Peer Christian Kunstmann (2014)

Studia Mathematica

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Given a strongly continuous semigroup ${(S (t))}_{t \geq 0}$ on a Banach space X with generator A and an element f ∈ D(A²) satisfying $| | S (t) f | | \leq e^{- ω t} | | f | |$ and $| | S (t) A ² f | | \leq e^{- ω t} | | A ² f | |$ for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.

Operator theoretic properties of semigroups in terms of their generators

S. Blunck, L. Weis (2001)

Studia Mathematica

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Let $(T_{t})$ be a C₀ semigroup with generator A on a Banach space X and let be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to if and only if the integrated semigroup $S_{t} : = \int_{0}^{t} T_{s} d s$ belongs to . For analytic semigroups, $S_{t} \in$ implies $T_{t} \in$ , and in this case we give precise estimates for the growth of the -norm of $T_{t}$ (e.g. the trace of $T_{t}$ ) in terms of the resolvent growth and the imbedding D(A) ↪ X.

On the K-theory of the $C^{*}$ -algebra generated by the left regular representation of an Ore semigroup

Joachim Cuntz, Siegfried Echterhoff, Xin Li (2015)

Journal of the European Mathematical Society

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We compute the $K$ -theory of $C^{*}$ -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the $K$ -theory of these semigroup $C^{*}$ -algebras in terms of the $K$ -theory for the reduced group $C^{*}$ -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.

On domains with ACC on invertible ideals

Stefania Gabelli (1988)

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

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If $A$ is a domain with the ascending chain condition on (integral) invertible ideals, then the group $I(A)$ of its invertible ideals is generated by the set $I_{m}(A)$ of maximal invertible ideals. In this note we study some properties of $I_{m}(A)$ and we prove that, if $I(A)$ is a free group on $I_{m}(A)$ , then $A$ is a locally factorial Krull domain.

Semiproper ideals

Hiroshi Sakai (2005)

Fundamenta Mathematicae

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We say that an ideal I on $_{κ} λ$ is semiproper if the corresponding poset $ℙ_{I}$ is semiproper. In this paper we investigate properties of semiproper ideals on $_{κ} λ$ .

Semigroups generated by convex combinations of several Feller generators in models of mathematical biology

Adam Bobrowski, Radosław Bogucki (2008)

Studia Mathematica

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Let be a locally compact Hausdorff space. Let $A_{i}$ , i = 0,1,...,N, be generators of Feller semigroups in C₀() with related Feller processes $X_{i} = X_{i} (t), t \geq 0$ and let $α_{i}$ , i = 0,...,N, be non-negative continuous functions on with $\sum_{i = 0}^{N} α_{i} = 1$ . Assume that the closure A of $\sum_{k = 0}^{N} α_{k} A_{k}$ defined on $⋂_{i = 0}^{N} (A_{i})$ generates a Feller semigroup T(t), t ≥ 0 in C₀(). A natural interpretation of a related Feller process X = X(t), t ≥ 0 is that it evolves according to the following heuristic rules: conditional on being at a point p ∈ , with probability...

Erratum to “Can $ℬ (ℓ^{p})$ ever be amenable?” (Studia Math. 188 (2008), 151-174)

Matthew Daws, Volker Runde (2009)

Studia Mathematica

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On norm closed ideals in $L (ℓ_{p}, ℓ_{q})$

B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky (2007)

Studia Mathematica

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It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for $X = ℓ_{p}$ (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of $L (ℓ_{p} \oplus ℓ_{q})$ for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in $L (ℓ_{p}, ℓ_{q})$ for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in $L (ℓ_{p}, ℓ_{q})$ , including one that has not been studied before. The proofs use various methods...

On domains with ACC on invertible ideals

Stefania Gabelli (1988)

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

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Semigroups whose proper subsemigroups are $Π$ -regular

T. Malinović (1989)

Matematički Vesnik

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The algebra of the subspace semigroup of $M ₂ (_{q})$

Jan Okniński (2002)

Colloquium Mathematicae

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The semigroup $S = S (M ₂ (_{q}))$ of subspaces of the algebra $M ₂ (_{q})$ of 2 × 2 matrices over a finite field $_{q}$ is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.

Two ideals connected with strong right upper porosity at a point

Viktoriia Bilet, Oleksiy Dovgoshey, Jürgen Prestin (2015)

Czechoslovak Mathematical Journal

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Let $SP$ be the set of upper strongly porous at $0$ subsets of $ℝ^{+}$ and let $\hat{I} (SP)$ be the intersection of maximal ideals $I \subseteq SP$ . Some characteristic properties of sets $E \in \hat{I} (SP)$ are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at $0$ subsets of $ℝ^{+}$ is a proper subideal of $\hat{I} (SP) .$ Earlier, completely strongly porous sets and some of their properties...

Effective Nullstellensatz for arbitrary ideals

János Kollár (1999)

Journal of the European Mathematical Society

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Let $f_{i}$ be polynomials in $n$ variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials $g_{i}$ such that $\sum g_{i} f_{i} = 1$ . The effective versions of this result bound the degrees of the $g_{i}$ in terms of the degrees of the $f_{j}$ . The aim of this paper is to generalize this to the case when the $f_{i}$ are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.

Algebra in the superextensions of twinic groups

Taras Banakh, Volodymyr Gavrylkiv

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Given a group X we study the algebraic structure of the compact right-topological semigroup λ(X) consisting of all maximal linked systems on X. This semigroup contains the semigroup β(X) of ultrafilters as a closed subsemigroup. We construct a faithful representation of the semigroup λ(X) in the semigroup ${(X)}^{(X)}$ of all self-maps of the power-set (X) and show that the image of λ(X) in ${(X)}^{(X)}$ coincides with the semigroup $E n d_{λ} ((X))$ of all functions f: (X) → (X) that are equivariant, monotone and symmetric...

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 $F^{t}$ .

Growth of semigroups in discrete and continuous time

Alexander Gomilko, Hans Zwart, Niels Besseling (2011)

Studia Mathematica

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We show that the growth rates of solutions of the abstract differential equations ẋ(t) = Ax(t), $ẋ (t) = A^{- 1} x (t)$ , and the difference equation $x_{d} (n + 1) = (A + I) {(A - I)}^{- 1} x_{d} (n)$ are closely related. Assuming that A generates an exponentially stable semigroup, we show that on a general Banach space the lowest growth rate of the semigroup ${(e^{A^{- 1} t})}_{t \geq 0}$ is O(∜t), and for $((A + I) {(A - I)}^{- 1}) ⁿ$ it is O(∜n). The similarity in growth holds for all Banach spaces. In particular, for Hilbert spaces the best estimates are O(log(t)) and O(log(n)), respectively. Furthermore,...

On ${(m, n)}_{T}$ ideals and subgroups of a semigroup

D. N. Krgović (1977)

Matematički Vesnik

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Sums of commuting operators with maximal regularity

Christian Le Merdy, Arnaud Simard (2001)

Studia Mathematica

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Let Y be a Banach space and let $S \subset L_{p}$ be a subspace of an $L_{p}$ space, for some p ∈ (1,∞). We consider two operators B and C acting on S and Y respectively and satisfying the so-called maximal regularity property. Let ℬ and be their natural extensions to $S (Y) \subset L_{p} (Y)$ . We investigate conditions that imply that ℬ + is closed and has the maximal regularity property. Extending theorems of Lamberton and Weis, we show in particular that this holds if Y is a UMD Banach lattice and $e^{- t B}$ is a positive contraction...