Isomorphic classification of $L_{p,q}$-spaces: the case $p=2,\ 1\leq q< 2$
HTML articles powered by AMS MathViewer
- by O. Sadovskaya and F. Sukochev
- Proc. Amer. Math. Soc. 146 (2018), 3975-3984
- DOI: https://doi.org/10.1090/proc/14058
- Published electronically: April 4, 2018
- PDF | Request permission
Abstract:
Let $1\leq q<2$. We prove that the Banach space $l_{2,q}$ (respectively, $L_{2,q}(0,\infty )$) does not isomorphically embed into the space $L_{2,q}(0,1)$ (respectively, $L_{2,q}(0,1)\oplus l_{2,q}$).References
- S. V. Astashkin and F. A. Sukochev, Banach-Saks property in Marcinkiewicz spaces, J. Math. Anal. Appl. 336 (2007), no. 2, 1231–1258. MR 2353012, DOI 10.1016/j.jmaa.2007.03.040
- Jöran Bergh and Jörgen Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. MR 0482275, DOI 10.1007/978-3-642-66451-9
- N. L. Carothers and S. J. Dilworth, Subspaces of $L_{p,q}$, Proc. Amer. Math. Soc. 104 (1988), no. 2, 537–545. MR 962825, DOI 10.1090/S0002-9939-1988-0962825-8
- S. J. Dilworth, Special Banach lattices and their applications, Handbook of the geometry of Banach spaces, Vol. I, North-Holland, Amsterdam, 2001, pp. 497–532. MR 1863700, DOI 10.1016/S1874-5849(01)80014-0
- P. G. Dodds, E. M. Semenov, and F. A. Sukochev, The Banach-Saks property in rearrangement invariant spaces, Studia Math. 162 (2004), no. 3, 263–294. MR 2047655, DOI 10.4064/sm162-3-6
- S. G. Kreĭn, Yu. Ī. Petunīn, and E. M. Semënov, Interpolation of linear operators, Translations of Mathematical Monographs, vol. 54, American Mathematical Society, Providence, R.I., 1982. Translated from the Russian by J. Szűcs. MR 649411
- A. Kuryakov and F. Sukochev, Isomorphic classification of $L_{p,q}$-spaces, J. Funct. Anal. 269 (2015), no. 8, 2611–2630. MR 3390012, DOI 10.1016/j.jfa.2015.06.012
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367, DOI 10.1007/978-3-662-35347-9
- E. M. Semënov and F. A. Sukochev, The Banach-Saks index, Mat. Sb. 195 (2004), no. 2, 117–140 (Russian, with Russian summary); English transl., Sb. Math. 195 (2004), no. 1-2, 263–285. MR 2068953, DOI 10.1070/SM2004v195n02ABEH000802
Bibliographic Information
- O. Sadovskaya
- Affiliation: Institute of Mathematics of Uzbekistan Academy of Sciences, Tashkent, 100084, Uzbekistan
- Email: sadovskaya-o@inbox.ru
- F. Sukochev
- Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia
- MR Author ID: 229620
- Email: f.sukochev@unsw.edu.au
- Received by editor(s): October 25, 2017
- Received by editor(s) in revised form: December 12, 2017
- Published electronically: April 4, 2018
- Communicated by: Thomas Schlumprecht
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3975-3984
- MSC (2010): Primary 46E30
- DOI: https://doi.org/10.1090/proc/14058
- MathSciNet review: 3825850