Semi-Characters of the Multiplicative Semigroup of Integers Modulo $m$

Bohumír Parízek; Štefan Schwarz

Displaying similar documents to “Semi-Characters of the Multiplicative Semigroup of Integers Modulo $m$ ”

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...

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 $F^{t}$ .

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 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...

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.

On upper triangular nonnegative matrices

Yizhi Chen, Xian Zhong Zhao, Zhongzhu Liu (2015)

Czechoslovak Mathematical Journal

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We first investigate factorizations of elements of the semigroup $S$ of upper triangular matrices with nonnegative entries and nonzero determinant, provide a formula for $ρ (S)$ , and, given $A \in S$ , also provide formulas for $l (A)$ , $L (A)$ and $ρ (A)$ . As a consequence, open problem 2 and problem 4 presented in N. Baeth et al. (2011), are partly answered. Secondly, we study the semigroup of upper triangular matrices with only positive integral entries, compute some invariants of such semigroup, and also partly answer...

Some model theory of SL(2,ℝ)

Jakub Gismatullin, Davide Penazzi, Anand Pillay (2015)

Fundamenta Mathematicae

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We study the action of G = SL(2,ℝ), viewed as a group definable in the structure M = (ℝ,+,×), on its type space $S_{G} (M)$ . We identify a minimal closed G-flow I and an idempotent r ∈ I (with respect to the Ellis semigroup structure * on $S_{G} (M)$ ). We also show that the “Ellis group” (r*I,*) is nontrivial, in fact it is the group with two elements, yielding a negative answer to a question of Newelski.

Spaces of multipliers and their preduals for the order multiplication on [0, 1]

Savita Bhatnagar, H. L. Vasudeva (2002)

Colloquium Mathematicae

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Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), $L^{p} (I)$ , 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise $H o m_{C (I)} (L^{r} (I), L^{p} (I))$ and their preduals.

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.

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

Dogan Çömez (1989)

Colloquium Mathematicae

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On pairwise semi $R_{0}$ and pairwise semi $R_{1}$ bitopological spaces

M. Jelić (1982)

Matematički Vesnik

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Some generalisations of $T_{D}$ spaces

S. P. Arya, M. P. Bhamini (1982)

Matematički Vesnik

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On some free semigroups, generated by matrices

Piotr Słanina (2015)

Czechoslovak Mathematical Journal

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Let $A = [\begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}], B_{λ} = [\begin{matrix} 1 & 0 \\ λ & 1 \end{matrix}] .$ We call a complex number $λ$ “semigroup free“ if the semigroup generated by $A$ and $B_{λ}$ is free and “free” if the group generated by $A$ and $B_{λ}$ is free. First families of semigroup free $λ$ ’s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free $λ$ ’s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common...

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.

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...

Spaces of multipliers and their preduals for the order multiplication on [0,1]. II

Savita Bhatnagar (2004)

Colloquium Mathematicae

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Consider I = [0,1] as a compact topological semigroup with max multiplication and usual topology, and let $C (I), L^{p} (I), 1 \leq p \leq \infty$ , be the associated algebras. The aim of this paper is to study the spaces $H o m_{C (I)} (L^{r} (I), L^{p} (I))$ , r > p, and their preduals.

Displaying similar documents to “Semi-Characters of the Multiplicative Semigroup of Integers Modulo m ”

Displaying similar documents to “Semi-Characters of the Multiplicative Semigroup of Integers Modulo $m$ ”