A class of Banach sequence spaces analogous to the space of Popov
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 3, page 573-582
- ISSN: 0011-4642
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topAzimi, Parviz, and Ledari, A. A.. "A class of Banach sequence spaces analogous to the space of Popov." Czechoslovak Mathematical Journal 59.3 (2009): 573-582. <http://eudml.org/doc/37942>.
@article{Azimi2009,
abstract = {Hagler and the first named author introduced a class of hereditarily $l_1$ Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily $l_p$ Banach spaces for $1\le p<\infty $. Here we use these spaces to introduce a new class of hereditarily $l_p(c_0)$ Banach spaces analogous of the space of Popov. In particular, for $p=1$ the spaces are further examples of hereditarily $l_1$ Banach spaces failing the Schur property.},
author = {Azimi, Parviz, Ledari, A. A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Banach spaces; Schur property; hereditarily $l_p$; Banach space; Schur property; hereditarily },
language = {eng},
number = {3},
pages = {573-582},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A class of Banach sequence spaces analogous to the space of Popov},
url = {http://eudml.org/doc/37942},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Azimi, Parviz
AU - Ledari, A. A.
TI - A class of Banach sequence spaces analogous to the space of Popov
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 573
EP - 582
AB - Hagler and the first named author introduced a class of hereditarily $l_1$ Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily $l_p$ Banach spaces for $1\le p<\infty $. Here we use these spaces to introduce a new class of hereditarily $l_p(c_0)$ Banach spaces analogous of the space of Popov. In particular, for $p=1$ the spaces are further examples of hereditarily $l_1$ Banach spaces failing the Schur property.
LA - eng
KW - Banach spaces; Schur property; hereditarily $l_p$; Banach space; Schur property; hereditarily
UR - http://eudml.org/doc/37942
ER -
References
top- Azimi, P., A new class of Banach sequence spaces, Bull. of Iranian Math. Society 28 (2002), 57-68. (2002) Zbl1035.46006MR1992259
- Azimi, P., Hagler, J., 10.2140/pjm.1986.122.287, Pacific J. Math. 122 (1986), 287-297. (1986) MR0831114DOI10.2140/pjm.1986.122.287
- Bourgain, J., -subspace of Banach spaces, Lecture notes. Free University of Brussels.
- Lindenstrauss, J., Tzafriri, L., Classical Banach Spaces, Vol. I sequence Spaces, Springer Verlag, Berlin. Zbl0852.46015MR0415253
- Popov, M. M., 10.1090/S0002-9939-05-07758-0, Proc. Amer. Math. Soc. 133 (2005), 2023-2028. (2005) Zbl1080.46007MR2137868DOI10.1090/S0002-9939-05-07758-0
- Popov, M. M., More examples of hereditarily Banach spaces, Ukrainian Math. Bull. 2 (2005), 95-111. (2005) Zbl1166.46304MR2172327
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