Pointwise absolutely convergent series of operators and related classes of Banach spaces
Liudmyla Kadets; Vladimir Kadets
Open Mathematics (2012)
- Volume: 10, Issue: 2, page 603-608
- ISSN: 2391-5455
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Abstract
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topLiudmyla Kadets, and Vladimir Kadets. "Pointwise absolutely convergent series of operators and related classes of Banach spaces." Open Mathematics 10.2 (2012): 603-608. <http://eudml.org/doc/269528>.
@article{LiudmylaKadets2012,
abstract = {We study classes of operators represented as a pointwise absolutely convergent series of simpler ones, starting with rank 1 operators. In this short note we address the question, how far the repetition of this procedure can lead.},
author = {Liudmyla Kadets, Vladimir Kadets},
journal = {Open Mathematics},
keywords = {Pointwise absolute convergence; Operator series; Dunford-Pettis operators; pointwise absolutely convergent series; Schur property},
language = {eng},
number = {2},
pages = {603-608},
title = {Pointwise absolutely convergent series of operators and related classes of Banach spaces},
url = {http://eudml.org/doc/269528},
volume = {10},
year = {2012},
}
TY - JOUR
AU - Liudmyla Kadets
AU - Vladimir Kadets
TI - Pointwise absolutely convergent series of operators and related classes of Banach spaces
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 603
EP - 608
AB - We study classes of operators represented as a pointwise absolutely convergent series of simpler ones, starting with rank 1 operators. In this short note we address the question, how far the repetition of this procedure can lead.
LA - eng
KW - Pointwise absolute convergence; Operator series; Dunford-Pettis operators; pointwise absolutely convergent series; Schur property
UR - http://eudml.org/doc/269528
ER -
References
top- [1] Kadets V.M., A Course in Functional Analysis, Kharkov State University, Kharkov, 2006 (in Russian) Zbl1128.46001
- [2] Kadets V., Kalton N., Werner D., Unconditionally convergent series of operators and narrow operators on L 1, Bull. London Math. Soc., 2005, 37(2), 265–274 http://dx.doi.org/10.1112/S0024609304003881 Zbl1077.46008
- [3] Lindenstrauss J., Tzafriri L., Classical Banach Spaces. I, Ergeb. Math. Grenzgeb., 92, Springer, Berlin-New York, 1977 Zbl0362.46013
- [4] Maslyuchenko O.V., Mykhaylyuk V.V., Popov M.M., A lattice approach to narrow operators, Positivity, 2009, 13(3), 459–495 http://dx.doi.org/10.1007/s11117-008-2193-z Zbl1183.47033
- [5] Rosenthal H.P., Embeddings of L 1 in L 1, In: Conference in Modern Analysis and Probability, New Haven, June 8–11, 1982, Contemp. Math., 26, American Mathematical Society, Providence, 1984, 335–349
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