In this note we survey the partial results needed to show the following general theorem: is a family of mutually non isomorphic Banach spaces. We also comment some related facts and open problems.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1176,
author = {Pilar Cembranos and Jose Mendoza},
title = {On the mutually non isomorphic $l\_{p}(l\_{q})$
},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {36},
year = {2016},
pages = {117-127},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1176}
}
Pilar Cembranos; Jose Mendoza. On the mutually non isomorphic $l_{p}(l_{q})$
. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 36 (2016) pp. 117-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1176/
[000] [1] F. Albiac and J.L. Ansorena, On the mutually non isomorphic spaces, II, Math. Nachr. 288 (2015), 5-9. doi: 10.1002/mana.201300161 | Zbl 1327.46004
[001] [2] F. Albiac and N.J. Kalton, Topics in Banach space theory (Graduate Texts in Mathematics, 233, Springer, New York, 2006). | Zbl 06566917
[002] [3] J. Bourgain, P.G. Casazza, J. Lindenstrauss and L. Tzafriri, Banach spaces with a unique unconditional basis, up to permutation, Mem. Amer. Math. Soc. 54, no. 322 (1985). | Zbl 0575.46011
[003] [4] P. Cembranos and J. Mendoza, Banach spaces of vector-valued functions (Lecture Notes in Mathematics 1676, Springer-Verlag, Berlin, 1997). | Zbl 0902.46017
[004] [5] ,P. Cembranos and J. Mendoza, and are not isomorphic, J. Math. Anal. Appl. 341 (2008), 295-297. doi: 10.1016/j.jmaa.2007.10.027 | Zbl 1139.46020
[005] [6] P. Cembranos and J. Mendoza, The Banach spaces and are not isomorphic, J. Math. Anal. Appl. 367 (2010), 361-363. doi: 10.1016/j.jmaa.2010.01.057
[006] [7] P. Cembranos and J. Mendoza, On the mutually non isomorphic spaces, Math. Nachr. 284 (2011), 2013-2023. doi: 10.1002/mana.201010056 | Zbl 1234.46007
[007] [8] J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators,Cambridge Studies in Advanced Mathematics, 43 (Cambridge University Press, Cambridge, 1995). | Zbl 0855.47016
[008] [9] W.B. Johnson, A complementary universal conjugate Banach space and its relation to the approximation problem, Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces (Jerusalem, 1972). Israel J. Math. 13 (1972), 301-310. doi: 10.1007/BF02762804
[009] [10] T.E. Khmyleva, On the isomorphism of spaces of bounded continuous functions (Russian. English summary), Investigations on linear operators and the theory of functions, XI. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI),113,1981,243-246. Translated in Journal of Soviet Mathematics, 22 (1983), 1860-1862. doi: 10.1007/BF01882590 | Zbl 0489.46015
[010] [11] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I (Ergebnisse der Mathematik und ihrer Grenzgebiete vol. 92, Springer-Verlag, 1977). | Zbl 0362.46013
[011] [12] J. Motos, M.J. Planells and C.F. Talavera, On some iterated weighted spaces, J. Math. Anal. Appl. 338 (2008), 162-174. doi: 10.1016/j.jmaa.2007.05.009 | Zbl 1145.46022
[012] [13] J. Motos and M.J. Planells, On sequence space representations of Hörmander-Beurling spaces, J. Math. Anal. Appl. 348 (2008), 395-403. doi: 10.1016/j.jmaa.2008.07.031 | Zbl 1162.46024
[013] [14] A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209-228. | Zbl 0104.08503
[014] [15] H. Triebel, Interpolation theory, function spaces, differential operators (VEB Deutscher Verlag der Wissenschaften, Berlin and North-Holland Publishing Co., Amsterdam-New York 1978 (First editions). Johann Ambrosius Barth, Heidelberg 1995 (Second edition)).