V. M. Kadets, M. M. Popov, “Some stability theorems on narrow operators acting in $L_1$ and $C(K)$”, Mat. Fiz. Anal. Geom., 2003, Volume 10, Number 1,Pages 49

This article is cited in 10 papers

Some stability theorems on narrow operators acting in $L_1$ and $C(K)$

V. M. Kadets^a, M. M. Popov^b

^a Department of Mechanics and Mathematics, V. N. Karazin Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine
^b Department of Mechanics and Mathematics, Chernivtsi National University, 2 Kotsiubyns'kogo Str., Chernivtsi, 58012, Ukraine

Abstract: 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.

MSC: 46B20, 46B04, 47B38

Received: 28.02.2002

Language: English