Approximating points of a Banach space by points of an operator image

Taras Banakh, Yuriy Golovaty


Answering one problem that has its origins in quantum mechanics, we prove that for any sequence Ann of convex nowhere dense sets in a Banach space X and any sequence εnn=1 of positive real numbers with limnεn=0, the set A=xX:n aAn  x-a<εn is nowhere dense in X.

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