Detalles de Evento
- IMAG Functional Analysis Seminar
- Title: Lineability, spaceability and Orlicz-Lorentz spaces.
- By Juan Seoane (Universidad Complutense de Madrid)
- Abstract: Vladimir Gurariy showed (1966) that the set of Weierstrass' monsters (classical continuous nowhere differentiable functions) contains (up to the zero function) infinite dimensional linear spaces. On top of that, in 1999, he (jointly with V. Fonf and M. Kadets) showed that, when working within C[0,1], the above infinite dimensional linear space can be chosen to be closed in C[0,1]. These results led Gurariy (2005) to coin the terms “lineability” and “spaceability” (MSC2020: 15A03 and 46B87). The idea behind it is, in a nutshell, to answer the following questions: How common are “bad” properties? And… what do we mean by “common” in the previous question? And by “bad”?Lately, quite a few works have been focusing on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying certain special properties. This trend has caught the eye of several researchers within Real and Complex Analysis, Operator Theory, Summability Theory, Polynomials in Banach spaces, Axiomatic Set Theory, Probability Theory, and Functional Analysis. Throughout this talk we shall present a brief account on some classical results in this topic as well as some recent joint works on nonlinear subsets of Orlicz-Lorentz spaces with Luis Bernal-González, Daniel L. Rodríguez-Vidanes, and Hyung-Joon Tag.
