Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 1, pp. 49-60
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V. M. Kadets; M. M. Popov. Some stability theorems on narrow operators acting in $L_1$ and $C(K)$. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 1, pp. 49-60. http://geodesic.mathdoc.fr/item/JMAG_2003_10_1_a4/
@article{JMAG_2003_10_1_a4,
author = {V. M. Kadets and M. M. Popov},
title = {Some stability theorems on narrow operators acting in $L_1$ and~$C(K)$},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {49--60},
year = {2003},
volume = {10},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2003_10_1_a4/}
}
TY - JOUR
AU - V. M. Kadets
AU - M. M. Popov
TI - Some stability theorems on narrow operators acting in $L_1$ and $C(K)$
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 2003
SP - 49
EP - 60
VL - 10
IS - 1
UR - http://geodesic.mathdoc.fr/item/JMAG_2003_10_1_a4/
LA - en
ID - JMAG_2003_10_1_a4
ER -
%0 Journal Article
%A V. M. Kadets
%A M. M. Popov
%T Some stability theorems on narrow operators acting in $L_1$ and $C(K)$
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2003
%P 49-60
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2003_10_1_a4/
%G en
%F JMAG_2003_10_1_a4
A new proof of two stability theorems concerning narrow operators acting from $L_1$ to $L_1$ or from $C(K)$ to an arbitrary Banach space is given. Namely a sum of two such operators and moreover a sum of a point-wise unconditionally convergent series of such operators is a narrow operator again. The relations between several possible definitions of narrow operators on $L_1$ are also discussed.
