An Application of Kadets-Pelczynski Sets to Narrow Operators

作者：Krasikova I V^*; Popov M M

来源：Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii, 2013, 9(1): 102-107.

• narrow operator
• Kothe function space
• Banach space L-p

A known analogue of the pitt compactness theorem for function spaces asserts that if 1 <= p < 2 and p< r < proportional to, then every operator T : L-p -> L-r is narrow. Using a technique developed by M.I. Kadets and A. Pelczynski, we prove a similar result. More precisely, if 1 <= p < 2 and F is a Kothe-Banach space on [0, 1] with an absolutely continuous norm containing no isomorph of L-p such that F subset of L-p, then every regular operator T : L-p -> F is narrow

• 出版日期2013