Data: wtorek, 29.03.2022, godz. 10:30-12:30
Prelegent: prof. dr hab. Grzegorz Lewicki (Instytut Matematyki UJ)
Abstrakt: Let \(X\) be a real or complex Banach space and let \(Y\subset X\) be a finite-dimensional subspace. Fix \(A\in \mathcal{L}(Y)\). Then we define \[\mathcal{P}_A (X, Y ) = \{P\in \mathcal{L}(X, Y ) : P|_Y = A\}.\] An operator \(P_o \in \mathcal{P}_A (X, Y)\) is called a minimal extension (a minimal projection) if \[\|P_o\| = \inf\{|P | : P \in \mathcal{P}_A (X, Y)\}.\] The aim of this talk is to present some characterizations of minimal extensions, which generalize previously obtained results for minimal projections. Also some new applications of the above mentioned criteria for minimal projections will be presented.