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Matematicheskie Zametki, 1997, Volume 62, Issue 2, Pages 223–237
DOI: https://doi.org/10.4213/mzm1607 (Mi mzm1607) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Ultrametric spaces and related Hilbert spaces

R. S. Ismagilov

N. E. Bauman Moscow State Technical University
Full-text PDF (239 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm1607
Abstract: We present simple proofs of the possibility of embedding ultrametric spaces in Hilbert spaces. The main part of the paper deals with ultrametric spaces that we call totally infinite spaces. Related Hilbert spaces, automorphisms of totally infinite spaces, and the corresponding linear operators are considered.
Received: 06.03.1996
English version:
Mathematical Notes, 1997, Volume 62, Issue 2, Pages 186–197
DOI: https://doi.org/10.1007/BF02355907
Bibliographic databases:
UDC: 517.518
Language: Russian
Citation: R. S. Ismagilov, “Ultrametric spaces and related Hilbert spaces”, Mat. Zametki, 62:2 (1997), 223–237; Math. Notes, 62:2 (1997), 186–197
Citation in format AMSBIB
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\paper Ultrametric spaces and related Hilbert spaces
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\issue 2
\pages 223--237
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\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 2
\pages 186--197
\crossref{https://doi.org/10.1007/BF02355907}
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  • https://doi.org/10.4213/mzm1607
  • https://www.mathnet.ru/eng/mzm/v62/i2/p223
    • This publication is cited in the following 5 articles:
    1. Surinder Pal Singh Kainth, A Comprehensive Textbook on Metric Spaces, 2023, 243  crossref
    2. Lemin, AJ, “The category of ultrametric spaces is isomorphic to the category of complete, atomic, tree-like, and real graduated lattices LAT”, Algebra Universalis, 50:1 (2003), 35  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Lemin A., Lemin V., “On Metrically Universal Ultrametric Spaces Lv Tau and Lw Tau”, Ultrametric Functional Analysis, Contemporary Mathematics Series, 319, eds. Schikhof W., PerezGarcia C., Escassut A., Amer Mathematical Soc, 2003, 191–205  crossref  mathscinet  zmath  isi
    4. Lemin A., “Spectral Decomposition of Ultrametric Spaces and Topos Theory”, Topology Proceedings, Monographic Series, 26, no. 2, eds. Gruenhage G., Heath J., Kennedy J., Minc P., Reed G., Shakhmatov D., Slaminka E., Tuncali M., Auburn Univ, 2002, 721–739  mathscinet  zmath  adsnasa  isi
    5. O. L. Semenova, A. A. Florinskii, “Ideals of porous sets in the real line and in metrizable topological spaces”, J Math Sci, 102:5 (2000), 4508  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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