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Matematicheskie Zametki, 2006, Volume 79, Issue 3, Pages 339–352
DOI: https://doi.org/10.4213/mzm2704 (Mi mzm2704) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Extremally distant normed spaces with additional restrictions

F. L. Bakharev

Saint-Petersburg State University
Full-text PDF (262 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm2704
Abstract: We study the relationship between the Banach—Mazur distance and the modified Banach—Mazur distance. We sharpen the Szarek theorem on the construction of invariant norms with specific properties and construct extremally distant normed spaces with norms invariant under groups of automorphisms of small cardinality. We prove that the trivial upper bound for the Banach—Mazur distance obtained in terms of the modified Banach—Mazur distance is order-sharp.
Received: 10.08.2004
Revised: 12.03.2005
English version:
Mathematical Notes, 2006, Volume 79, Issue 3, Pages 314–326
DOI: https://doi.org/10.1007/s11006-006-0036-4
Bibliographic databases:
UDC: 517.98
Language: Russian
Citation: F. L. Bakharev, “Extremally distant normed spaces with additional restrictions”, Mat. Zametki, 79:3 (2006), 339–352; Math. Notes, 79:3 (2006), 314–326
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm2704
  • https://www.mathnet.ru/eng/mzm/v79/i3/p339
    • This publication is cited in the following 3 articles:
    1. A. I. Khrabrov, “Volume ratio for the Cartesian product of convex bodies”, St. Petersburg Math. J., 32:5 (2021), 905–916  mathnet  crossref
    2. F. L. Bakharev, “Generalization of some classical results to the case of the modified Banach–Mazur distance”, J. Math. Sci. (N. Y.), 141:5 (2007), 1517–1525  mathnet  crossref  mathscinet  zmath  elib  elib
    3. F. L. Bakharev, “Estimation of maximal distances between spaces with norms invariant under a group of operators”, J. Math. Sci. (N. Y.), 141:5 (2007), 1526–1530  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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