On the plasticity of the unit spheres of ${\mathrm{\ell }}_1$, ${\mathrm{\ell }}_{\mathrm{\infty }}$, $c$, and Hilbert spaces

This paper demonstrates the expand-contract plasticity of the unit spheres of ${\mathrm{\ell }}_1$, ${\mathrm{\ell }}_{\mathrm{\infty }}$, and $c$. Furthermore, it establishes the strong plasticity of the unit spheres of Hilbert spaces.