We prove that Banach spaces ℓ1 ⊕2 R and X ⊕∞ Y , with strictly convex X and Y , have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).
We prove that Banach spaces ℓ 1 ⊕ 2 R and X ⊕∞ Y , with strictly convex X and Y , have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).
We prove the plasticity of the unit ball of c. That is, we show that every non-expansive bijection from the unit ball of c onto itself is an isometry. We also demonstrate a slightly weaker property for the unit ball of c 0 -we prove that a non-expansive bijection is an isometry, provided that it has a continuous inverse. 2020 Mathematics Subject Classification. 46B20, 47H09.
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