SUCCESSIVE RADII OF FAMILIES OF CONVEX BODIES

We study properties of the so-called inner and outer successive radii of special families of convex bodies. First we consider the balls of the $p$-norms, for which we show that the precise value of the outer (inner) radii when $p\geq 2$ ($1\leq p\leq 2$), as well as bounds in the contrary case $1\leq p\leq 2$ ($p\geq 2$), can be obtained as consequences of known results on Gelfand and Kolmogorov numbers of identity operators between finite-dimensional normed spaces. We also prove properties that successive radii satisfy when we restrict to the families of the constant width sets and the $p$-tangential bodies.