New compound geometric invariants are constructed in order to characterize complemented embeddings of Cartesian products of power series spaces. Bessaga's conjecture is proved for the same class of spaces.
@article{bwmeta1.element.bwnjournal-article-smv137i1p33bwm,
author = {P. Chalov and P. Djakov and V. Zahariuta},
title = {Compound invariants and embeddings of Cartesian products},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {33-47},
zbl = {0951.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv137i1p33bwm}
}
Chalov, P.; Djakov, P.; Zahariuta, V. Compound invariants and embeddings of Cartesian products. Studia Mathematica, Tome 133 (1999) pp. 33-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv137i1p33bwm/
[00000] [1] B C. Bessaga, Some remarks on Dragilev's theorem, Studia Math. 31 (1968), 307-318. | Zbl 0182.45301
[00001] [2] C. Bessaga, A. Pełczyński and S. Rolewicz, On diametral approximative dimension and linear homogeneity of F-spaces, Bull. Acad. Polon. Sci. 9 (1961), 677-683. | Zbl 0109.33502
[00002] [3] P. B. Djakov, A short proof of the theorem on quasi-equivalence of regular bases, Studia Math. 55 (1975), 269-271. | Zbl 0317.46007
[00003] [4] P. B. Djakov, M. Yurdakul and V. P. Zahariuta, On Cartesian products of Köthe spaces, Bull. Polish Acad. Sci. 43 (1996), 113-117. | Zbl 0835.46004
[00004] [5] P. B. Djakov, M. Yurdakul and V. P. Zahariuta, Isomorphic classification of Cartesian products of power series spaces, Michigan Math. J. 43 (1996), 221-229. | Zbl 0890.46008
[00005] [6] M. M. Dragilev, On regular bases in nuclear spaces, Mat. Sb. 68 (1965), 153-173 (in Russian).
[00006] [7] M. M. Dragilev, Bases in Köthe Spaces, Rostov-na-Donu, 1983 (in Russian).
[00007] [8] A. N. Kolmogorov, On the linear dimension of topological vector spaces, Dokl. Akad. Nauk SSSR 120 (1958), 239-241 (in Russian). | Zbl 0080.31203
[00008] [9] V. P. Kondakov, Problems of Geometry of Nonnormable Spaces, Rostov State University, Rostov-na-Donu, 1983 (in Russian). | Zbl 0614.46004
[00009] [10] V. P. Kondakov, On structure of unconditional bases in some Köthe spaces, Studia Math. 76 (1983), 137-151 (in Russian). | Zbl 0539.46010
[00010] [11] V. P. Kondakov and V. P. Zahariuta, On weak equivalence of bases in Köthe spaces, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Ser. Estestv. Nauk 4 (1982), 110-115 (in Russian).
[00011] [12] B. S. Mityagin, Approximative dimension and bases in nuclear spaces, Uspekhi Mat. Nauk 16 (1961), no. 4, 63-132 (in Russian). | Zbl 0104.08601
[00012] [13] B. S. Mityagin, Sur l'équivalence des bases inconditionnelles dans les échelles de Hilbert, C. R. Acad. Sci. Paris 269 (1969), 426-428. | Zbl 0186.44704
[00013] [14] B. S. Mityagin, Equivalence of bases in Hilbert scales, Studia Math. 37 (1970), 111-137 (in Russian).
[00014] [15] B. S. Mityagin, Non-Schwarzian power series spaces, Math. Z. 182 (1983), 303-310. | Zbl 0541.46007
[00015] [16] A. Pełczyński, On the approximation of S-spaces by finite-dimensional spaces, Bull. Acad. Polon. Sci. 5 (1957), 879-881. | Zbl 0078.28703
[00016] [17] M. Yurdakul and V. P. Zahariuta, Linear topological invariants and isomorphic classification of Cartesian products of locally convex spaces, Turkish J. Math. 19 (1995), 37-47. | Zbl 0861.46005
[00017] [18] V. P. Zahariuta, On isomorphisms of Cartesian products of linear topological spaces, Funktsional. Anal. i Prilozhen. 4 (1970), no. 2, 87-88 (in Russian).
[00018] [19] V. P. Zahariuta, On the isomorphism of Cartesian products of locally convex spaces, Studia Math. 46 (1973), 201-221.
[00019] [20] V. P. Zahariuta, Linear topological invariants and isomorphisms of spaces of analytic functions, in: Matem. Analiz i ego Prilozhen. Rostov Univ., Vol. 2 (1970), 3-13, Vol. 3 (1971), 176-180 (in Russian).
[00020] [21] V. P. Zahariuta, Generalized Mityagin invariants and a continuum of pairwise nonisomorphic spaces of analytic functions, Funktsional. Anal. i Prilozhen. 11 (1977), no. 3, 24-30 (in Russian).
[00021] [22] V. P. Zahariuta, Synthetic diameters and linear topological invariants, in: School on the Theory of Operators in Function Spaces (abstracts of reports), Minsk, 1978, 51-52 (in Russian).
[00022] [23] V. P. Zahariuta, Linear Topological Invariants and Their Application to Generalized Power Spaces, Rostov Univ., 1979 (in Russian).
[00023] [24] V. P. Zahariuta, Linear topological invariants and their application to isomorphic classification of generalized power spaces, Turkish J. Math. 2 (1996), 237-289. | Zbl 0866.46005