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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 1998, Volume 5, Number 3/4, Pages 297–303 (Mi jmag442)  
On an isometric representation with the maximal set of spectral subspaces

G. M. Feldmana, G. Murazb

a Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., 310164, Kharkov, Ukraine
b Université de Grenoble 1, Institut Fourier, BP.7438402, St-Martin d'hères Cedex, France
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Abstract: It was proved the theorem. Let $G$ be a locally compact noncompact separable Abelian group. Then there exists an isometric representation of the group $G$ in a Banach space $X$ without eigenvectors for which any spectral subspace $L(K)\ne\{0\}$ if $K$ contains a nonempty perfect subset.
Received: 03.04.1998
Bibliographic databases:
Document Type: Article
Language: English
Citation: G. M. Feldman, G. Muraz, “On an isometric representation with the maximal set of spectral subspaces”, Mat. Fiz. Anal. Geom., 5:3/4 (1998), 297–303
Citation in format AMSBIB
\Bibitem{FelMur98}
\by G.~M.~Feldman, G.~Muraz
\paper On an isometric representation with the maximal set of spectral subspaces
\jour Mat. Fiz. Anal. Geom.
\yr 1998
\vol 5
\issue 3/4
\pages 297--303
\mathnet{http://mi.mathnet.ru/jmag442}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1668957}
\zmath{https://zbmath.org/?q=an:0956.22004}
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