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

Savita Bhatnagar

Displaying similar documents to “Spaces of multipliers and their preduals for the order multiplication on [0,1]. II”

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 left $ϕ$ -biflat Banach algebras

Amir Sahami, Mehdi Rostami, Abdolrasoul Pourabbas (2020)

Commentationes Mathematicae Universitatis Carolinae

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We study the notion of left $ϕ$ -biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra $S (G)$ is left $ϕ$ -biflat if and only if $G$ is amenable. Also we characterize left $ϕ$ -biflatness of semigroup algebra $l^{1} (S)$ in terms of biflatness, when $S$ is a Clifford semigroup.

On the continuity of the elements of the Ellis semigroup and other properties

Salvador García-Ferreira, Yackelin Rodríguez-López, Carlos Uzcátegui (2021)

Commentationes Mathematicae Universitatis Carolinae

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We consider discrete dynamical systems whose phase spaces are compact metrizable countable spaces. In the first part of the article, we study some properties that guarantee the continuity of all functions of the corresponding Ellis semigroup. For instance, if every accumulation point of $X$ is fixed, we give a necessary and sufficient condition on a point $a \in X^{'}$ in order that all functions of the Ellis semigroup $E (X, f)$ be continuous at the given point $a$ . In the second part, we consider transitive...

$R_{0}$ and $R_{1}$ topological spaces

C. Dorsett (1978)

Matematički Vesnik

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On $R_{0}$ and $R_{1}$ topological spaces

D. Janković (1981)

Matematički Vesnik

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A note on $R_{0}$ and $R_{1}$ topological spaces

M. R. Žižović (1986)

Matematički Vesnik

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Trivialization of $𝒞 (X)$ -algebras with strongly self-absorbing fibres

Marius Dadarlat, Wilhelm Winter (2008)

Bulletin de la Société Mathématique de France

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Suppose $A$ is a separable unital $𝒞 (X)$ -algebra each fibre of which is isomorphic to the same strongly self-absorbing and $K_{1}$ -injective $C^{*}$ -algebra $𝒟$ . We show that $A$ and $𝒞 (X) \otimes 𝒟$ are isomorphic as $𝒞 (X)$ -algebras provided the compact Hausdorff space $X$ is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.

Non supercyclic subsets of linear isometries on Banach spaces of analytic functions

Abbas Moradi, Karim Hedayatian, Bahram Khani Robati, Mohammad Ansari (2015)

Czechoslovak Mathematical Journal

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Let $X$ be a Banach space of analytic functions on the open unit disk and $Γ$ a subset of linear isometries on $X$ . Sufficient conditions are given for non-supercyclicity of $Γ$ . In particular, we show that the semigroup of linear isometries on the spaces $S^{p}$ ( $p > 1$ ), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space $H^{p}$ or the Bergman space $L_{a}^{p}$ ( $1 < p < \infty$ , $p \neq 2$ )...

A countably cellular topological group all of whose countable subsets are closed need not be $ℝ$ -factorizable

Mihail G. Tkachenko (2023)

Commentationes Mathematicae Universitatis Carolinae

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We construct a Hausdorff topological group $G$ such that $ℵ_{1}$ is a precalibre of $G$ (hence, $G$ has countable cellularity), all countable subsets of $G$ are closed and $C$ -embedded in $G$ , but $G$ is not $ℝ$ -factorizable. This solves Problem 8.6.3 from the book “Topological Groups and Related Structures" (2008) in the negative.

The covariety of perfect numerical semigroups with fixed Frobenius number

María Ángeles Moreno-Frías, José Carlos Rosales (2024)

Czechoslovak Mathematical Journal

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Let $S$ be a numerical semigroup. We say that $h \in ℕ ∖ S$ is an isolated gap of $S$ if ${h - 1, h + 1} \subseteq S .$ A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by $m (S)$ the multiplicity of a numerical semigroup $S$ . A covariety is a nonempty family $𝒞$ of numerical semigroups that fulfills the following conditions: there exists the minimum of $𝒞,$ the intersection of two elements of $𝒞$ is again an element of $𝒞$ , and $S ∖ {m (S)} \in 𝒞$ for all $S \in 𝒞$ such that $S \neq min (𝒞) .$ We prove that the set $𝒫 (F) = {S : S$ is a perfect numerical semigroup...

$H^{\infty}$ calculus and dilatations

Andreas M. Fröhlich, Lutz Weis (2006)

Bulletin de la Société Mathématique de France

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We characterise the boundedness of the $H^{\infty}$ calculus of a sectorial operator in terms of dilation theorems. We show e. g. that if $- A$ generates a bounded analytic $C_{0}$ semigroup $(T_{t})$ on a UMD space, then the $H^{\infty}$ calculus of $A$ is bounded if and only if $(T_{t})$ has a dilation to a bounded group on $L^{2} ([0, 1], X)$ . This generalises a Hilbert space result of C.LeMerdy. If $X$ is an $L^{p}$ space we can choose another $L^{p}$ space in place of $L^{2} ([0, 1], X)$ .

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.