Data: 14.10.2025 (wtorek), godz. 10.00
Miejsce: A1-33/34
Prelegent: prof. dr hab. Grzegorz Lewicki, Uniwersytet Jagieloński
Abstrakt:
Let \(X\) be a finite-dimensional normed space and let \(Y\subset X\) be its proper linear subspace. Denote by \(P(X, Y )\) the set of all linear projections from \(X\) onto \(Y\). Let us define
\( P_{Min}={P\in P(X,Y): ||P||=\lambda(Y,X)},\) where \(\lambda(Y,X)=\inf{||P||: P\in P(X,Y)},\)
(in other words the set of all minimal projections). The aim of this talk is to present some results concerning the affine dimension of the set \(P_{Min}(X, Y )\). We establish several results on the possible value of this dimension. We prove optimal upper bounds in terms of the dimension of \(X\) and \(Y\). Moreover, we improve these estimates in the polyhedral normed spaces. My talk is based on a joint work with Tomasz Kobos.