Almost periodic compactifications of group extensions

H. D. Junghenn; Paul Milnes

Displaying similar documents to “Almost periodic compactifications of group extensions”

Characterising weakly almost periodic functionals on the measure algebra

Matthew Daws (2011)

Studia Mathematica

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Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say $K_{W A P}$ . In this paper, we investigate properties of $K_{W A P}$ . We present a short proof that $K_{W A P}$ can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens...

On the size of quotients of function spaces on a topological group

Ahmed Bouziad, Mahmoud Filali (2011)

Studia Mathematica

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For a non-precompact topological group G, we consider the space C(G) of bounded, continuous, scalar-valued functions on G with the supremum norm, together with the subspace LMC(G) of left multiplicatively continuous functions, the subspace LUC(G) of left norm continuous functions, and the subspace WAP(G) of weakly almost periodic functions. We establish that the quotient space LUC(G)/WAP(G) contains a linear isometric copy of $ℓ_{\infty}$ , and that the quotient space C(G)/LMC(G) (and a fortiori...

Functionals on Banach Algebras with Scattered Spectra

H. S. Mustafayev (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let A be a complex, commutative Banach algebra and let $M_{A}$ be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space $M_{A}$ is scattered (i.e., $M_{A}$ has no nonempty perfect subset). (b) Weakly almost periodic...

Generalized $c$ -almost periodic type functions in $ℝ^{n}$

M. Kostić (2021)

Archivum Mathematicum

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In this paper, we analyze multi-dimensional quasi-asymptotically $c$ -almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl $c$ -almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically $c$ -almost periodic functions and reconsider the notion of semi- $c$ -periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide...

Remotely $c$ -almost periodic type functions in $ℝ^{n}$

Marco Kostić, Vipin Kumar (2022)

Archivum Mathematicum

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In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$ -almost periodic functions in $ℝ^{n},$ slowly oscillating functions in $ℝ^{n},$ and further analyze the recently introduced class of quasi-asymptotically $c$ -almost periodic...

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.

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 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...

A class of $I_{0}$ -sets

David Grow (1987)

Colloquium Mathematicae

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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...

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.

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.

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.

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 $F^{t}$ .

A version of the law of large numbers

Katusi Fukuyama (2001)

Colloquium Mathematicae

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By the method of Rio [10], for a locally square integrable periodic function f, we prove $(f (μ ₁^{t} x) + . . . + f (μ ₙ^{t} x)) / n \to \int_{0}^{1} f$ for almost every x and t > 0.

Existence and uniqueness of periodic solutions for odd-order ordinary differential equations

Yongxiang Li, He Yang (2011)

Annales Polonici Mathematici

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The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation $u^{(2 n + 1)} = f (t, u, u^{'}, . . ., u^{(2 n)})$ , where $f : ℝ \times ℝ^{2 n + 1} \to ℝ$ is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity $f (t, x ₀, x ₁, . . ., x_{2 n})$ to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].

On Hartman almost periodic functions

Guy Cohen, Viktor Losert (2006)

Studia Mathematica

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We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in $ℝ^{d}$ or $ℤ^{d}$ . We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure...

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.

Topologies on groups determined by right cancellable ultrafilters

Igor V. Protasov (2009)

Commentationes Mathematicae Universitatis Carolinae

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For every discrete group $G$ , the Stone-Čech compactification $β G$ of $G$ has a natural structure of a compact right topological semigroup. An ultrafilter $p \in G^{*}$ , where $G^{*} = β G ∖ G$ , is called right cancellable if, given any $q, r \in G^{*}$ , $q p = r p$ implies $q = r$ . For every right cancellable ultrafilter $p \in G^{*}$ , we denote by $G (p)$ the group $G$ endowed with the strongest left invariant topology in which $p$ converges to the identity of $G$ . For any countable group $G$ and any right cancellable ultrafilters $p, q \in G^{*}$ , we show that $G (p)$ is homeomorphic to $G (q)$ if...