Abstract
AbstractIt is well known that every $$l_2$$
l
2
-strictly singular operator from $$L_p$$
L
p
, $$1<p<\infty $$
1
<
p
<
∞
to any Banach space X with an unconditional basis is narrow. In this article, we extend this result to the setting of Banach spaces without an unconditional basis. We show that if $$1 \le p,r <\infty $$
1
≤
p
,
r
<
∞
, then every $$\ell _2$$
ℓ
2
-strictly singular operator T from $$L_p $$
L
p
into the Schatten–von Neumann r-class $$C_r$$
C
r
is narrow. This is a noncommutative complement to results in Mykhaylyuk et al. (in Israel J Math 203:81–108, 2014).
Funder
Australian research Council
Publisher
Springer Science and Business Media LLC
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