Isomorphisms of Cartesian products of l-power series spaces

• Autorzy: Karapinar E. , Yurdakul M. , Zahariuta V.
• Języki publikacji: EN

Abstrakty

EN

Let l be a Banach sequence space with a monotone norm [...], in which the canonical system (ei) is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products E[...](a) x E[...][b) where E[...](a) = K[...] and oE[...](b) = K[...) are finite and infinite l-power series spaces, respectively. This classification is the generalization of the results by Chalov et al. [Studia Math. 137 (1999)] and Djakov et al. [Michigan Math. J. 43 (1996)] by using the method of compound linear topological invariants developed by the third author.

Słowa kluczowe

EN

Cartesian products; l-power series spaces; compound linear topological invariants

PL

iloczyn kartezjański

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: Vol. 54, no 2
• Strony: 103--111
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Karapinar E.

autor

Yurdakul M.

autor

Zahariuta V.

• Izmir University of Economics Izmir, Turkey,

Bibliografia

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• [2] P. A. Chalov, P. B. Djakov and V. P. Zahariuta, Compound invaiants and embeddings of Cartesian products, Studia Math 137 (1999), 33-47.
• [3] P. B. Djakov, M. Yurdakul and V. P. Zahariuta, Isomorphic classification of Cartesian products, Michigan Math. J. 43 (1996), 221-229.
• [4] M. M. Dragilev, Bases in Kothe spaces, Rostov State Univ., Rostov-na-Donu, 1983 (in Russian).
• [5] S. G. Krein, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Amer. Math. Soc., Providence, RI, 1978.
• [6] B. S. Mityagin, Sur I'equivalence des bases inconditionnelles dans les echelles de Hilbert, C. R. Acad. Sci. Paris 269 (1969), 426-428.
• [7] —, The equivalence of bases in Hilbert scales, Studia Math. 37 (1970), 111-137 (in Russian).
• [8] V. P. Zahariuta, Linear topological invariants and isomorphisms of spaces of analytic functions, in: Mathematical Anal. Appl., Rostov State Univ., Rostov-na-Donu, 2 (1970), 3-13; 3 (1971), 176-180 (in Russian).
• [9] —, Generalized Mityagin invariants and a continuum of mutually nonisomorphic spaces of analytic functions, Funktsional. Anal. i Prilozhen. 11 (1977), 24-30 (in Russian).
• [10] —, Linear topologic invariants and their applications to isomorphic classification of generalized power spaces, Turkish J. Math. 20 (1996), 237-289.