18. April 2024, 15:00 until 17:00
AKOR Seminar: Surjectivity and invertibility of non-smooth maps between Banach spaces, Jesús A. Jaramillo, Universidad Complutense de Madrid
In the setting of Banach spaces, we address the problem of surjectivity, existence of a continuous section and invertibility for mappings which admit a suitable pseudo-Jacobian. We obtain a general sufficient condition for the existence of a continuous section. As a consequence, we recover from our result the classical Bartle-Graves selection theorem. We also obtain a sufficient condition for local invertibility, which in particular applies to the case of Gâteaux-differentiable maps. (Based on joint work with M. Ivanov, S. Lajara and N. Zlateva.)