Construction of the interpolation functor in the category of Freschet spaces with common basis

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2014.1.7425 Construction of the interpolation functor in the category of Freschet spaces with common basis Shubarin M. A. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 1. Abstract: 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 K\"othe spaces are described. Keywords: interpolations linear operators, interpolation functors, diagonal operators, Kothe spaces Language: Russian Download the full text For citation: Shubarin M. A. Construction of the interpolation functor in the category of Freschet spaces with common basis. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 1, pp.68-79. DOI 10.23671/VNC.2014.1.7425 + References 1. Bukur I., Deljanu A. Vvedenie v Teoriju Kategorij i Funktorov [Introduction to the Theory of Categories and Functors], Moskva, Mir, 1972, 259 p. (Russian). 2. Kadampatta S. N. Shkaly Lokal'no Vypuklyh Prostranstv i Prodolzhaemye Bazisy v Prostranstvah Analiticheskih Funkcij, Diss. ... Kand. Fiz.-Mat. Nauk, Rostov n/D., 1984, 250 p. (Russian). 3. Kadampatta S. N. Shkaly prostranstv analiticheskih funkcij. Izv. Sev.-Kavl. NC Vyssh. Shk., 1975, no. 4, pp. 64-68 (Russian). 4. Krejn S. G., Petunin Ju. I., Semenov E. M. Interpoljacija Linejnyh Operatorov [Interpolation of Linear Operators], Moskva, Nauka, 1978, 400 p. (Russian). 5. Krejn S. G., Semenov E. M., Brudnyj Ju. A. Interpolation of linear operators. J. of Soviet Mathematics, 1988, vol. 42, no. 6, pp. 2009-2112. 6. Tribel' H. Teorija Interpoljacii. Funkcional'nye Prostranstva. Differencial'nye Operatory [Interpolation Theory. Function Spaces. Differential Operators], Moskva, Mir, 1980, 664 p. (Russian). 7. Shubarin M. A. Interpolation conditions for families of Fréchet spaces. Vladikavk. Mat. Zhurn. [Vladikavk. Math. J.], 2007, vol. 9, no. 2, pp. 57-65 (Russian). 8. Shubarin M. A. Klassy prostranstv, porozhdaemye interpoljaciej diagonal'nyh operatorov. Izv. Vuzov. Sev.-Kavk. Region. Ser. Estestv. Nauki [Univ. News North-Caucasian Region. Natural Sci. Ser.], 2006, no. 1, pp. 24-26 (Russian). 9. Shubarin M. A. Obobshhennaja Teorema Aronshajna - Gal'jardo, Moskva, 2007. Dep. v VINITI, no. 446-V2007 (Russian). 10. Shubarin M. A. Extension of interpolation functors in categories of Frechét spaces. Mat. Forum. JuFO. Vol. 1. Issledovanija po Mat. Analizu [Math. Forum. SFU. Vol. 1. Studies on Math. Analysis], Vladikavkaz, VNC RAN i RSO-A, 2008, pp. 229-238 (Russian). 11. Arouszajn N., Gagliardo E. Interpolation spaces and interpolation methods. Ann. Mat. Pur. Appl., 1965, vol. 68, ser. 4, pp. 51-117. 12. Aytuna A., Djakov P. B., Goncharov A. P., Terziouglu T., Zahariuta V. P. Some open problem in the theory of locally convex spaces. Linear Topological Spaces and Complex Analysis I, Ankara, Metu-Tubitak, 1994, pp. 147-165. 13. Deutsch N. Interpolation dans les espaces vectorieles topologiques localement convexes. Mem. de la Soc. Math. de France, 1968, vol. 13, pp. 3-187. 14. Zahariuta V. Linear topologic invariants and their applications to isomorphic classification of generalized power spaces. Turkish J. Math., 1996, vol. 20, pp. 237-289. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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