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Mat. Sb., 2009, Volume 200, Number 2, Pages 75–88 (Mi msb4527)  

This article is cited in 3 scientific papers (total in 3 papers)

Constructions of regular algebras $\mathscr L_p^w(G)$

Yu. N. Kuznetsova

All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences

Abstract: A criterion for (Shilov) regularity of weighted algebras ${\mathscr L}_1^w(G)$ on a locally compact Abelian group $G$ is known from works of Beurling (1949) and Domar (1956). In the present paper this criterion is extended to translation-invariant weighted algebras $\mathscr L_p^w(G)$ with $p>1$. Regular algebras $\mathscr L_p^w(G)$ are constructed on any $\sigma$-compact Abelian group $G$. It was proved earlier by the author that $\sigma$-compactness is necessary (in the Abelian case) for the existence of weighted algebras $\mathscr L_p^w(G)$ with $p>1$.
Bibliography: 11 titles.

Keywords: locally compact Abelian group, regular algebra, Beurling algebras, weighted algebras.

DOI: https://doi.org/10.4213/sm4527

Full text: PDF file (530 kB)
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English version:
Sbornik: Mathematics, 2009, 200:2, 229–241

Bibliographic databases:

UDC: 517.986.62
MSC: Primary 46J10; Secondary 22B99
Received: 28.02.2008 and 12.09.2008

Citation: Yu. N. Kuznetsova, “Constructions of regular algebras $\mathscr L_p^w(G)$”, Mat. Sb., 200:2 (2009), 75–88; Sb. Math., 200:2 (2009), 229–241

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Gorin, “Regularity of group algebras”, Sb. Math., 200:8 (2009), 1165–1179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Kuznetsova Yu., Molitor-Braun C., “Harmonic analysis of weighted $L^p$-algebras”, Expo. Math., 30:2 (2012), 124–153  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. I. Akbarbaglu, M. Heydarpour, S. Maghsoudi, “Uniqueness of uniform norm and $C^*$-norm in $L_p(G,\omega)$”, Math. Slovaca, 64:2 (2014), 411–422  crossref  mathscinet  zmath  elib  scopus  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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