A proof of a theorem of Żelazko on $L^p$-algebras

K. Urbanik

Displaying similar documents to “A proof of a theorem of Żelazko on $L^{p}$ -algebras”

Unit groups of group algebras of some small groups

Gaohua Tang, Yangjiang Wei, Yuanlin Li (2014)

Czechoslovak Mathematical Journal

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Let $F G$ be a group algebra of a group $G$ over a field $F$ and $𝒰 (F G)$ the unit group of $F G$ . It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group $G$ with order $21$ over any finite field of characteristic $3$ is established. We also characterize the structure of the unit group of $F A_{4}$ over any finite field of characteristic $3$ and the...

Second duals of measure algebras

H. G. Dales, A. T.-M. Lau, D. Strauss

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Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L¹(G) and the measure algebra M(G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C₀(Ω)” of the C*-algebra C₀(Ω) for a locally compact space Ω, recognizing this space as C(Ω̃), where Ω̃ is the hyper-Stonean envelope of Ω. We shall study the C*-algebra $B^{b} (Ω)$ of bounded Borel functions on Ω, and we shall determine the exact cardinality of a variety...

Inertial subrings of a locally finite algebra

Yousef Alkhamees, Surjeet Singh (2002)

Colloquium Mathematicae

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I. S. Cohen proved that any commutative local noetherian ring R that is J(R)-adic complete admits a coefficient subring. Analogous to the concept of a coefficient subring is the concept of an inertial subring of an algebra A over a commutative ring K. In case K is a Hensel ring and the module $A_{K}$ is finitely generated, under some additional conditions, as proved by Azumaya, A admits an inertial subring. In this paper the question of existence of an inertial subring in a locally finite...

On the algebras $L_{p}$ of locally compact groups

Wiesław Żelazko (1961)

Colloquium Mathematicae

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Some properties of orders of quaternion algebras with regard to the discrete norm

Jan Horníček, Miroslav Kureš, Lenka Macálková (2016)

Mathematica Bohemica

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Quaternion algebras $(\frac{- 1, b}{ℚ})$ are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.

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...

Metric generalizations of Banach algebras

W. Żelazko

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CONTENTSPRELIMINARIES§ 0. Introduction.......................................................................................................................................................................3§ 1. Definitions and notation.................................................................................................................................................5Chapter ILOCALLY BOUNDED ALGEBRAS§ 2. Basic facts and examples..............................................................................................................................................6§...

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...

Isomorphism of commutative group algebras of $p$ -mixed splitting groups over rings of characteristic zero

Peter Vassilev Danchev (2006)

Mathematica Bohemica

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Suppose $G$ is a $p$ -mixed splitting abelian group and $R$ is a commutative unitary ring of zero characteristic such that the prime number $p$ satisfies $p \notin inv (R) \cup zd (R)$ . Then $R (H)$ and $R (G)$ are canonically isomorphic $R$ -group algebras for any group $H$ precisely when $H$ and $G$ are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).

A note on group algebras of $p$ -primary abelian groups

William Ullery (1995)

Commentationes Mathematicae Universitatis Carolinae

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Suppose $p$ is a prime number and $R$ is a commutative ring with unity of characteristic 0 in which $p$ is not a unit. Assume that $G$ and $H$ are $p$ -primary abelian groups such that the respective group algebras $R G$ and $R H$ are $R$ -isomorphic. Under certain restrictions on the ideal structure of $R$ , it is shown that $G$ and $H$ are isomorphic.

Displaying similar documents to “A proof of a theorem of Żelazko on L p -algebras”

Displaying similar documents to “A proof of a theorem of Żelazko on $L^{p}$ -algebras”