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. 
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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/

[1] Abanin A. V., “Vesovye prostranstva nepreryvnykh i golomorfnykh funktsii”, Tr. Mezhdunar. konf. «Matematicheskii analiz i matematicheskoe modelirovanie», YuMI VNTs RAN, Vladikavkaz, 2010, 15–20 | MR

[2] Dragilev M. M., “O pravilnykh bazisakh v yadernykh prostranstvakh”, Mat. sb., 68:3 (1965), 153–173 | Zbl

[3] Zakharyuta V. P., “Ob izimorfizme dekartovykh proizvedenii lineinykh topologicheskikh prostranstv”, Funkts. anal. prilozh., 4:2 (1970), 87–89 | MR

[4] Zakharyuta V. P., “Nekotorye lineinye topologicheskie invarianty i izomorfizm tenzornykh proizvedenii tsentrov shkal”, Izv. SKNTs VSh. Ser. estestv. nauk., 4 (1974), 62–64

[5] Zakharyuta V. P., “Ekstremalnye plyurisubgarmonicheskie funktsii, gilbertovy shkaly i izomorfizm prostranstv analiticheskikh funktsii mnogikh peremennykh,”, Teor. funktsii, funkts. anal. prilozh. (Kharkov)., 19 (1974), 133–157 | Zbl

[6] Zakharyuta V. P., “Izomorfizmy prostranstv analiticheskikh funktsii”, Dokl. AN SSSR., 255:1 (1980), 11–14 | MR | Zbl

[7] Kolmogorov A. N., “O lineinoi razmernosti topologicheskikh vektornykh prostranstv”, Dokl. AN SSSR., 120:2 (1958), 239–241 | Zbl

[8] Mityagin B. S., “Ekvivalentnost bazisov v gilbertovykh shkalakh”, Stud. Math., 37 (1971), 111–137 | DOI | Zbl

[9] Tribel Kh., Teoriya interpolyatsii, Funktsionalnye prostranstva. Differentsialnye operatory, Mir, M., 1980

[10] Shubarin M. A., “Operatornye idealy, opredelyaemye invariantnymi klassami prostranstv Freshe”, Mat. forum (Itogi nauki. Yug Rossii)., 8 (2013), 100–112

[11] Bessaga C., Pelczynski A., Rolewciz S., “On diametral approximative dimension und linear homogeneity of F-spaces”, Bull. Acad. Pol. Sci., 9 (1961), 677–683 | MR | Zbl

[12] Bessaga C., Pelczynski A., Rolewicz S., “Approximative dimension of liner topological spaces and some of its applications”, Stud. Math., Ser. Spec., 1 (1963), 26–29 | MR

[13] Bierstedt K. D., Bonet J., “Weighted $(LF)$-spaces of continuous functions”, Math. Nachr., 165 (1994), 25–48 | DOI | MR | Zbl

[14] Bierstedt K. D., Meise R., Summers V. H., “A projective descriptions of weighted inductive limits”, Trans. Am. Math. Soc., 272:1, 107–160 | DOI | MR | Zbl

[15] Cwikel M., Lecture notes on duality and interpolation spaces, arXiv: 0803.3558v2 [math.FA] | MR

[16] Meise R., Vogt D., Introduction to Functional Analysis, Clarendon Press, Oxford, 1997 | MR | Zbl

[17] Pelczynski A., “On the approximation of S-spaces by finite dimension space”, Bull. Acad. Pol. Sci., 5:9 (1957), 879–881 | MR | Zbl

[18] Rolewicz S., “On spaces of holomorphic functions”, Stud. Math., 21:2 (1962), 135–160 | DOI | MR

[19] Vogt D., “Charakterisierung der Unterräume vons”, Math. Z., 155 (1977), 109–117 | DOI | MR | Zbl

[20] Vogt D., “Frecheträume, zwishen denen jede stetige linear Abbildung beschränkt ist”, J. Reine Angew. Math., 345 (1983), 182–200 | MR | Zbl

[21] Vogt D., Wagner M. J., “Charakterisierung der Unterräume und Quotientenräume der nuclearen stabilen Potenzreihenräumen von unendlichem Typ”, Stud. Math., 70 (1981), 63–80 | DOI | MR | Zbl

[22] Wagner M.-J., “Quotientenräume von stabilen Potenzreihenrümen endlichen Typs”, Manuscr. Math., 31 (1980), 97–109 | DOI | MR | Zbl

[23] Zachariuta V. P., “On isomorphism of Cartesian products of local convex spaces”, Stud. Math., 46 (1973), 201–221 | DOI | MR

[24] Zahariuta V., “Linear topologic invariants and their applications to isomorphic classification of generalized power spaces”, Tr. J. Math., 20 (1996), 237–289 | MR | Zbl