Around Discontinuity for the Riesz Projection in the Uniform Metric

The present paper is based on a lecture given by the author at the conference ‘‘Complex Analysis and Related Problems’’ (Kazan, Russia, June 29–July 4, 2022). The lecture was devoted to the Glicksberg conjecture and a related but independent assertion that the sums of certain ideals in a uniform alg...

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Published inLobachevskii journal of mathematics Vol. 44; no. 10; pp. 4537 - 4545
Main Author Kislyakov, S. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.10.2023
Springer Nature B.V
Subjects
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Riesz projection
Glicksberg conjecture
nonclosed sums
Hardy–Lebesgue pairs
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Abstract The present paper is based on a lecture given by the author at the conference ‘‘Complex Analysis and Related Problems’’ (Kazan, Russia, June 29–July 4, 2022). The lecture was devoted to the Glicksberg conjecture and a related but independent assertion that the sums of certain ideals in a uniform algebra are never closed. The present paper puts forward several new formulations in comparison with those given in the lecture and in the existing literature.
AbstractList The present paper is based on a lecture given by the author at the conference ‘‘Complex Analysis and Related Problems’’ (Kazan, Russia, June 29–July 4, 2022). The lecture was devoted to the Glicksberg conjecture and a related but independent assertion that the sums of certain ideals in a uniform algebra are never closed. The present paper puts forward several new formulations in comparison with those given in the lecture and in the existing literature.
Author Kislyakov, S. V.
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Cites_doi 10.2307/2034952
10.1090/S0002-9947-1964-0161175-8
10.1007/BF01461145
10.1017/CBO9780511526138
10.1007/BF02427719
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Issue 10
Keywords Riesz projection
Glicksberg conjecture
nonclosed sums
Hardy–Lebesgue pairs
Language English
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References Gamelin (CR7) 1969
Rudin (CR1) 1962; 13
Diestel, Jarchow, Tonge (CR10) 1995
CR2
Glicksberg (CR3) 1964; 111
Kislyakov, Zlotnikov (CR6) 2018; 44
Kislyakov (CR8) 1974; 18
Gamelin, Kislyakov (CR5) 2001
Kislyakov (CR4) 1990; 40
Kislyakov (CR9) 1981; 16
I. Glicksberg (7474_CR3) 1964; 111
T. W. Gamelin (7474_CR5) 2001
S. V. Kislyakov (7474_CR8) 1974; 18
W. Rudin (7474_CR1) 1962; 13
7474_CR2
S. V. Kislyakov (7474_CR6) 2018; 44
S. V. Kislyakov (7474_CR9) 1981; 16
S. V. Kislyakov (7474_CR4) 1990; 40
T. W. Gamelin (7474_CR7) 1969
J. Diestel (7474_CR10) 1995
References_xml – volume: 13
  start-page: 429
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  end-page: 432
  ident: CR1
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  publication-title: Proc. Am. Math. Soc.
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  ident: CR3
  article-title: Some uncomplemented function algebras
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  doi: 10.1090/S0002-9947-1964-0161175-8
  contributor:
    fullname: Glicksberg
– volume: 18
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  year: 1974
  end-page: 639
  ident: CR8
  article-title: Uncomplemented uniform algebras
  publication-title: Math. Notes
  doi: 10.1007/BF01461145
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    fullname: Kislyakov
– year: 1995
  ident: CR10
  doi: 10.1017/CBO9780511526138
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– volume: 16
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  article-title: Uniform algebras as Banach spaces
  publication-title: J. Math. Sci.
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  contributor:
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– ident: CR2
– year: 1969
  ident: CR7
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    fullname: Gamelin
– year: 2001
  ident: CR5
  doi: 10.1016/S1874-5849(01)80018-8
  contributor:
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– volume: 40
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  ident: CR4
  article-title: Proper uniform algebras are uncomplemented
  publication-title: Dokl. Math.
  contributor:
    fullname: Kislyakov
– volume: 44
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  doi: 10.1090/S0002-9947-1964-0161175-8
  contributor:
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– volume: 44
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  publication-title: Anal. Math.
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  publication-title: Proc. Am. Math. Soc.
  doi: 10.2307/2034952
  contributor:
    fullname: W. Rudin
– volume-title: Handbook of the Geometry of Banach Spaces
  year: 2001
  ident: 7474_CR5
  doi: 10.1016/S1874-5849(01)80018-8
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    fullname: T. W. Gamelin
– volume: 18
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  ident: 7474_CR8
  publication-title: Math. Notes
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    fullname: S. V. Kislyakov
– volume-title: Absolutely Summing Operators
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– volume-title: Uniform Algebras
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  ident: 7474_CR9
  publication-title: J. Math. Sci.
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StartPage 4537
SubjectTerms Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Title Around Discontinuity for the Riesz Projection in the Uniform Metric
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