Ball Proximinal and Strongly Ball Proximinal Spaces
نویسندگان
چکیده
Let Y be an E-proximinal (respectively, a strongly proximinal) subspace of X. We prove that Y is (strongly) ball proximinal in X if and only if for any x ∈ X with (x+ Y ) ∩BX 6= ∅, (x+ Y ) ∩BX is (strongly) proximinal in x+Y . Using this characterization and a smart construction, we obtain three Banach spaces Z ⊂ Y ⊂ X such that Z is ball proximinal in X and Y/Z is ball proximinal in X/Z, but Y is not ball proximinal in X. This solves a problem raised by Bandyopadhyay, Lin, and Rao [BLR] in 2007.
منابع مشابه
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