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
Reference26 articles.
1. Albiac, F., Kalton, N.: Topics in Banach space theory, Graduate Texts in Mathematics 233, Springer (2006)
2. Arazy, J.: Some remarks on interpolation theorems and the boundness of the triangular projection in unitary matrix spaces. Integr. Equa. Oper. Theo. 1(4), 453–495 (1978)
3. Arazy, J., Lindenstrauss, J.: Some linear topological properties of the spaces $$C_p$$ of operators on Hilbert space. Compos. Math. 30, 81–111 (1975)
4. Dodds, P., Ferleger, S., de Pagter, B., Sukochev, F.: Vilenkin systems and generalized triangular truncation operator. Intergral Equ. Oper. Theory 40, 403–435 (2001)
5. Fack, T.: Type and cotype inequalities for noncommutative $$L^p$$-spaces. J. Oper. Theory 17, 255–279 (1987)
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