## w$$^*$$-basic sequences and reflexivity of Banach spaces.(English)Zbl 1081.46017

Summary: We observe that a separable Banach space $$X$$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly, if $$\mathcal L(X,Y)$$ is not reflexive for reflexive $$X$$ and $$Y$$, then $$\mathcal L(X_1, Y)$$ is not reflexive for some $$X_1\subset X$$, $$X_1$$ having a basis.

### MSC:

 46B28 Spaces of operators; tensor products; approximation properties
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### References:

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