Geodesic
On the fullness conditions of the eigenvector system of general normal operators
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (1988), pp. 3-8

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In terms of almosl-pcriodicity of functions $\phi(T(g)x)$ with $T$-uniorder continuous representation of local compact Abel group $G$ of the $(C_0)$ class in weakly full linear topological space $X$, the criterion of fullness for $T$-representation eigenvectors has been proved. In case, when $X$ is reflexive Banach space and $T$ is an isometric representation of group G of $X$ space, with all weighted subspaces having finite dimensions, the existence of full functional system biorthogonal to the union of the basis vectors of weighted snbspace of $T$ representation has been proved. 
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     author = {M. I. Karakhanyan},
     title = {On the fullness conditions of the eigenvector system of general normal operators},
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M. I. Karakhanyan. On the fullness conditions of the eigenvector system of general normal operators. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (1988), pp. 3-8. http://geodesic.mathdoc.fr/item/UZERU_1988_3_a0/