Geodesic
Conditions for the nonisomorphism of a pair of weighted spaces of continuous functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 144-155

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In this paper, we formulate conditions for a pair of Fréchet spaces to be nonisomorphic. These conditions are formulated in terms of invariant classes of the spaces $(D_1)$ and $(D_2)$. As a consequence, we prove that weighted spaces of continuous functions of a special form are nonisomorphic. These spaces can be considered as a modification of spaces of power series of finite and infinite type.
Keywords: isomorphic spaces, bounded operator, real interpolation method, weighted space of continuous functions. 
@article{INTO_2021_190_a13,
     author = {M. A. Shubarin},
     title = {Conditions for the nonisomorphism of a pair of weighted spaces of continuous functions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {144--155},
     publisher = {mathdoc},
     volume = {190},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_190_a13/}
}
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M. A. Shubarin. Conditions for the nonisomorphism of a pair of weighted spaces of continuous functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 144-155. http://geodesic.mathdoc.fr/item/INTO_2021_190_a13/