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Unconditionally convergent series of operators and narrow operators on $L_1$

Vladimir Kadets·Nigel Kalton·Dirk Werner
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Abstract

We introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$ into a space with an unconditional basis belongs to this class.

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Vladimir Kadets, Nigel Kalton, Dirk Werner. 2003-11-19. Unconditionally convergent series of operators and narrow operators on $L_1$. https://arxiv.org/abs/math/0311324

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