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On the geometric properties of Cesàro spaces. (English. Russian original) Zbl 1253.46022
Sb. Math. 203, No. 4, 514-533 (2012); translation from Mat. Sb. 203, No. 4, 61-80 (2012).
By definition, the Cesàro space $$\mathrm{Ces}_p[0,1]$$ consists of all measurable functions $$f$$ on $$[0,1]$$ with $\|f\|_{C_p}= \left[\int_0^1\left(\frac{1}{t}\int_0^1|f(s)|ds\right)^pdt\right]^{1/p}<\infty, \quad 1\leq p<\infty.$ S. V. Astashkin and L. Maligranda [Indag. Math., New Ser. 20, No. 3, 329–379 (2009; Zbl 1200.46027)] give a description of the set of all $$q$$ for which isomorphic copies of $$\ell^q$$ are contained in $$\mathrm{Ces}_p[0,1]$$. The author considers complemented copies of $$\ell^q$$. He shows that $$\mathrm{Ces}_p[0,1]$$ contains a complemented copy of $$\ell^q$$ if and only if either $$q=1$$ or $$q=p$$. As a corollary, he obtains that $$\mathrm{Ces}_p[0,1]$$, $$p>1$$, contains no complemented copy of $$L_q[0,1]$$, $$q>1$$.

##### MSC:
 46B25 Classical Banach spaces in the general theory 46B42 Banach lattices
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