Event Details
- IMAG Functional Analysis Seminar
- Title: On some geometric properties of Banach spaces
- By Joanna Markowicz (University of the National Education Commission, Krakow, Poland)
- Abstract: The aim of the talk will be to present some results concerning selected properties of direct sums of Banach spaces and their applications. Among those properties we will study for instance uniform convexity, uniform smoothness, uniform nonsquareness, Opial properties and the García-Falset coefficient. In the results connected to geometric properties of direct sums of Banach spaces there are considered direct sums \(Y=\left(\sum_{i\in I}X_i\right)_E\), where \(\{X_i\}_{i\in I}\) is a family of Banach spaces and the norm in the direct sum comes from the Banach lattice $E$ that is named a substitutional space for the direct sum. In addition, we will study Banach lattices and their properties connected to the order such as uniform monotonicity and order uniform smoothness The talk will also consider preserving uniform convexity and the Opial property in interpolation spaces constructed with the use of a general abstract discrete \(K\)-method based on a space with an unconditional basis.
