Geodesic
Construction of the interpolation functor in the category of Freschet spaces with common basis
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 1, pp. 68-79 Cet article a éte moissonné depuis la source Math-Net.Ru

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A family of interpolating functors in the category of pairs of Frechet spaces with common absolute basis is constructed and its properties are studied. A reiteration type theorem is proved for this family. In terms of this interpolation functor some types of Köthe spaces are described. 
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M. A. Shubarin. Construction of the interpolation functor in the category of Freschet spaces with common basis. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 1, pp. 68-79. http://geodesic.mathdoc.fr/item/VMJ_2014_16_1_a7/

[1] Bukur I., Delyanu A., Vvedenie v teoriyu kategorii i funktorov, Mir, M., 1972, 259 pp. | MR

[2] Kadampatta S. N., Shkaly lokalno vypuklykh prostranstv i prodolzhaemye bazisy v prostranstvakh analiticheskikh funktsii, Diss. $\dots$ kand. fiz.-mat. nauk, Rostov n/D, 1984, 250 pp.

[3] Kadampatta S. N., “Shkaly prostranstv analiticheskikh funktsii”, Izv. SKNTs VSh, 1975, no. 4, 64–68 | MR

[4] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978, 400 pp. | MR

[5] Krein S. G., Semenov E. M., Brudnyi Yu. A., “Interpolyatsiya lineinykh operatorov”, Itogi nauki i tekhniki. Ser. Mat. analiz, 24, VINITI, M., 1986, 3–163 | MR | Zbl

[6] Tribel Kh., Teoriya interpolyatsii. Funktsionalnye prostranstva. Differentsialnye operatory, Mir, M., 1980, 664 pp. | MR

[7] Shubarin M. A., “Usloviya interpolyatsionnosti dlya semeistv prostranstv Freshe”, Vladikavk. mat. zhurn., 9:2 (2007), 54–62 | MR

[8] Shubarin M. A., “Klassy prostranstv, porozhdaemye interpolyatsiei diagonalnykh operatorov”, Izv. vuzov Sev. Kavk. regiona. Ser. estestv. nauki, 2006, no. 1, 24–26 | Zbl

[9] Shubarin M. A., Obobschennaya teorema Aronshaina–Galyardo, Dep. v VINITI, No 446-V2007, M., 2007

[10] Shubarin M. A., “Prodolzhenie interpolyatsionnykh funktorov v razlichnykh kategoriyakh prostranstv Freshe”, Issledovaniya po mat. analizu, Mat. forum. YuFO, 1, VNTs RAN i RSO-A, Vladikavkaz, 2008, 229–238

[11] Arouszajn N., Gagliardo E., “Interpolation spaces and interpolation methods”, Ann. Mat. Pur. Appl. (4), 68, (1965), 51–117 | DOI | MR

[12] Aytuna A., Djakov P. B., Goncharov A. P., Terzioğlu T., Zahariuta V. P., “Some open problem in the theory of locally convex spaces”, Linear Topological Spaces and Complex Analysis, v. I, Metu-Tübitak, Ankara, 1994, 147–165 | MR

[13] Deutsch N., “Interpolation dans les espaces vectorieles topologiques localement convexes”, Mémoires de la Société Mathématique de France, 13 (1968), 3–187 | MR

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