On sums of narrow operators on Köthe function spaces
On sums of narrow operators on Köthe function spaces
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关于 Köthe 函数空间上的窄算子之和
DOI：
10.1016/j.jmaa.2013.03.008
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发表时间：
2013
影响因子：
1.3
通讯作者：
M. Popov
中科院分区：
文献类型：
--
作者：
V. Mykhaylyuk;M. Popov
本文在[0，1]上的Köthe Banach空间E和Banach空间X上找到了两个从E到X的窄算子之和是窄算子的充要条件.利用这个条件，我们证明了：给定[0，1]上的Köthe Banach空间E，存在Banach空间X和具有非窄和T=T1+T2的窄算子T1，T2：E→X.特别是，这回答了一个关于V.M.的问题。Kadets和第二个命名的作者，是否对每个Banach空间X的两个窄算子从L1到X的总和必须是窄的。另一个结果是，对任意1<p≤∞，存在正则窄算子T1，T2：Lp→L∞，其非窄和T=T1+T2.对于p=∞，这回答了O.V. Maslyuchenko和作者的一个问题。
We find necessary and sufficient conditions on a Köthe Banach space E on [0,1] and a Banach space X under which a sum of two narrow operators from E to X is narrow. Using this condition, we prove that, given a Köthe Banach space E on [0,1], there exist a Banach space X and narrow operators T1,T2:E→X with non-narrow sum T=T1+T2. In particular, this answers in the negative, a question of V.M. Kadets and the second named author, of whether for every Banach space X a sum of two narrow operators from L1to X must be narrow. Another result asserts that for every 1<p≤∞ there are regular narrow operators T1,T2:Lp→L∞with non-narrow sum T=T1+T2. For p=∞ this answers a question of O.V. Maslyuchenko and the authors.