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Estimates of the diameters of certain sets in the Banach spaces and are given; in particular, the orders of the diameters, , 1 SRC=http: //ej. iop. org/images/0025-5726/11/2/A06/texᵢm₁719ᵢmg5. gif/>, are completely determined. Bibliography: 18 titles.
B S Kašin (Sat,) studied this question.
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