On Weak$$^*$$-Extensible Subspaces of Banach Spaces
نویسندگان
چکیده
Abstract Let X be a Banach space and $$Y \subseteq X$$ Y ⊆ X closed subspace. We prove that if the quotient / Y is weakly Lindelöf determined or weak Asplund, then for every $$w^*$$ w ∗ -convergent sequence $$(y_n^*)_{n\in \mathbb N}$$ ( y n ) ∈ N in $$Y^*$$ there exist subsequence $$(y_{n_k}^*)_{k\in k $$(x_k^*)_{k\in x $$X^*$$ such $$x_k^*|_Y=y_{n_k}^*$$ | = all $$k\in N$$ . As an application, we obtain Grothendieck whenever reflexive, which answers question raised by González Kania.
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ژورنال
عنوان ژورنال: Mediterranean Journal of Mathematics
سال: 2022
ISSN: ['1660-5454', '1660-5446']
DOI: https://doi.org/10.1007/s00009-022-01981-z