On some spaces of linear functionals on the algebras $A_ p(G)$ for locally compact groups

E. E. Granirer

Displaying similar documents to “On some spaces of linear functionals on the algebras $A_{p} (G)$ for locally compact groups”

A property for locally convex *-algebras related to property (T) and character amenability

Xiao Chen, Anthony To-Ming Lau, Chi-Keung Ng (2015)

Studia Mathematica

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For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let $C_{c} (G)$ be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that $(C_{c} (G), ε_{G})$ has property (FH) if and only if G has property...

Locally $G_{δ}$ -spaces

Zdeněk Frolík (1962)

Czechoslovak Mathematical Journal

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A note on locally convex spaces with a basic sequence of $β$ -disks

B. Mirković (1970)

Matematički Vesnik

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Connectivity functions defined on $I^{n}$

Richard G. Gibson, Fred Roush (1987)

Colloquium Mathematicae

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On generalized Beurling’s theorem and symmetry of $L_{1}$ -group algebras

Zenobia Anusiak (1971)

Colloquium Mathematicae

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Operator Figà-Talamanca-Herz algebras

Volker Runde (2003)

Studia Mathematica

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Let G be a locally compact group. We use the canonical operator space structure on the spaces $L^{p} (G)$ for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues $O A_{p} (G)$ of the classical Figà-Talamanca-Herz algebras $A_{p} (G)$ . If p ∈ (1,∞) is arbitrary, then $A_{p} (G) \subset O A_{p} (G)$ and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that $O A_{p} (G)$ is a completely contractive Banach algebra for each p ∈ (1,∞), and that $O A_{q} (G) \subset O A_{p} (G)$ completely contractively...

On cardinalities of algebras of formulas for $ω_{0}$ -categorical theories

Jan Waszkiewicz (1973)

Colloquium Mathematicae

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Algebras whose groups of units are Lie groups

Helge Glöckner (2002)

Studia Mathematica

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Let A be a locally convex, unital topological algebra whose group of units $A^{\times}$ is open and such that inversion $ι : A^{\times} \to A^{\times}$ is continuous. Then inversion is analytic, and thus $A^{\times}$ is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then $A^{\times}$ has a locally diffeomorphic exponential function and multiplication is given locally by the Baker-Campbell-Hausdorff series. In contrast, for suitable non-Mackey complete A, the unit group $A^{\times}$ is an analytic Lie...

Dual complementors in topological algebras

Marina Haralampidou (2005)

Banach Center Publications

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We deal with dual complementors on complemented topological (non-normed) algebras and give some characterizations of a dual pair of complementors for some classes of complemented topological algebras. The study of dual complementors shows their deep connection with dual algebras. In particular, we refer to Hausdorff annihilator locally C*-algebras and to proper Hausdorff orthocomplemented locally convex H*-algebras. These algebras admit, by their nature, the same type of dual pair of...

On a translation property of positive definite functions

Lars Omlor, Michael Leinert (2010)

Banach Center Publications

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If G is a locally compact group with a compact invariant neighbourhood of the identity e, the following property (*) holds: For every continuous positive definite function h≥ 0 with compact support there is a constant $C_{h} > 0$ such that $\int L_{x} h \cdot g \leq C_{h} \int h g$ for every continuous positive definite g≥0, where $L_{x}$ is left translation by x. In [L], property (*) was stated, but the above inequality was proved for special h only. That “for one h” implies “for all h” seemed obvious, but turned out not to be obvious at...

On locally $S$ -closed spaces

Takashi Noiri (1983)

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

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Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente $S$ -chiuso sia localmente $S$ -chiuso.

On locally $S$ -closed spaces

Takashi Noiri (1983)

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

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Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente $S$ -chiuso sia localmente $S$ -chiuso.

$ℵ_{0}$ -categoricity of products of 1-unary algebras

Philip Olin (1975)

Colloquium Mathematicae

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Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, Nico Spronk (2012)

Studia Mathematica

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For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras $A_{p} (G, ω)$ . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We...

A representation theorem for tense $n \times m$ -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

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In 2000, Figallo and Sanza introduced $n \times m$ -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$ -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class $_{n \times m}$ of tense $n \times m$ -valued Łukasiewicz-Moisil algebras (or tense LM $_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...

Singularity categories of skewed-gentle algebras

Xinhong Chen, Ming Lu (2015)

Colloquium Mathematicae

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Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let $(Q^{s g}, I^{s g})$ and $(Q^{g}, I^{g})$ be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra $K Q^{s g} / ⟨ I^{s g} ⟩$ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of $K Q^{g} / ⟨ I^{g} ⟩$ . As a corollary, we find that $g l d i m K Q^{s g} / ⟨ I^{s g} ⟩ < \infty$ if and only if $g l d i m K Q / ⟨ I ⟩ < \infty$ if and only if $g l d i m K Q^{g} / ⟨ I^{g} ⟩ < \infty$ .

On two-to-one continuous functions

J. Mioduszewski

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CONTENTSIntroduction................................................................................................................................................................................3I. General properties of k-to-one functions on locally compact spaces1. Multi-valued functions Ф and ψ......................................................................................................................................... 62. The proof of (I.11)..................................................................................................................................................................

Extension properties of Stone-Čech coronas and proper absolute extensors

A. Chigogidze (2013)

Fundamenta Mathematicae

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We characterize, in terms of X, the extensional dimension of the Stone-Čech corona βX∖X of a locally compact and Lindelöf space X. The non-Lindelöf case is also settled in terms of extending proper maps with values in $I^{τ} ∖ L$ , where L is a finite complex. Further, for a finite complex L, an uncountable cardinal τ and a $Z_{τ}$ -set X in the Tikhonov cube $I^{τ}$ we find a necessary and sufficient condition, in terms of $I^{τ} ∖ X$ , for X to be in the class AE([L]). We also introduce a concept of a proper absolute...

The local weight of an effective locally compact transformation group and the dimension of $L^{2} (G)$

J. de Vries (1978)

Colloquium Mathematicae

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A note on the commutator of two operators on a locally convex space

Edvard Kramar (2016)

Commentationes Mathematicae Universitatis Carolinae

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Denote by $C$ the commutator $A B - B A$ of two bounded operators $A$ and $B$ acting on a locally convex topological vector space. If $A C - C A = 0$ , we show that $C$ is a quasinilpotent operator and we prove that if $A C - C A$ is a compact operator, then $C$ is a Riesz operator.

Displaying similar documents to “On some spaces of linear functionals on the algebras A p ( G ) for locally compact groups”

Displaying similar documents to “On some spaces of linear functionals on the algebras $A_{p} (G)$ for locally compact groups”