RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Mat. Fiz. Anal. Geom.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 3/4, Pages 231–260 (Mi jmag494)  

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

Gårding domains for unitary representations of countable inductive limits of locally compact groups

A. I. Danilenko

Department of Mechanics and Mathematics, Kharkov State University, 4, Svobody Sq., 310077, Kharkov, Ukraine

Abstract: Let $G$ be the inductive limit of an increasing sequence of locally compact second countable groups $G_1\subset G_2\subset\cdots$. Given a strongly continuous unitary representation $U$ of $G$ in a separable Hilbert space $\mathcal H$, we construct an $U$-invariant, separable, nuclear, Montel $(\mathrm{DF})$-space $\mathcal F$ which is densely (topologically) embedded in $\mathcal H$ and such that the restriction of $U$ to $\mathcal F$ is a weakly continuous representation of $G$ by continuous linear operators in $\mathcal F$. Moreover, $\mathcal F$ is a domain of essential self-adjointness for the generator of each one-parameter subgroup of $G$, and all such generators keep $\mathcal F$ invariant.

Full text: PDF file (3488 kB)
Full text: http:/.../abstract.php?uid=m03-0231r
Received: 09.10.1995
Language:

Citation: A. I. Danilenko, “Gårding domains for unitary representations of countable inductive limits of locally compact groups”, Mat. Fiz. Anal. Geom., 3:3/4 (1996), 231–260

Citation in format AMSBIB
\Bibitem{Dan96}
\by A.~I.~Danilenko
\paper G{\aa}rding domains for unitary representations of countable inductive limits of locally compact groups
\jour Mat. Fiz. Anal. Geom.
\yr 1996
\vol 3
\issue 3/4
\pages 231--260
\mathnet{http://mi.mathnet.ru/jmag494}


Linking options:
  • http://mi.mathnet.ru/eng/jmag494
  • http://mi.mathnet.ru/eng/jmag/v3/i3/p231

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Beltita D., Neeb K.-H., “A Nonsmooth Continuous Unitary Representation of a Banach-Lie Group”, J. Lie Theory, 18:4 (2008), 933–936  mathscinet  zmath  isi
    2. Neeb K.-H., “On Differentiable Vectors for Representations of Infinite Dimensional Lie Groups”, J. Funct. Anal., 259:11 (2010), 2814–2855  crossref  mathscinet  zmath  isi  elib
    3. Dawson M., Olafsson G., “Conical Representations For Direct Limits of Symmetric Spaces”, Math. Z., 286:3-4 (2017), 1375–1419  crossref  mathscinet  zmath  isi  scopus
  • Number of views:
    This page:51
    Full text:17

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020