Abundance of transitive linear operators in infinite dimension

• Grant number: 19/20500-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: December 01, 2019
• End date: August 29, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Patricia Romano Cirilo
• Grantee: Felipe Hikari Kawahama
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil
• Associated research grant: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II, AP.TEM
• Associated scholarship(s): 21/08199-7 - Beyond transitivity for linear operators on infinite dimension, BE.EP.MS

Abstract

This master's scholarship proposal intends to investigate possible density aspects of hypercyclic operators, i.e., operators in infinite dimension spaces that have a dense orbit. In fact, it is known that in the topology obtained with the usual norm, hypercyclics operators are nowhere dense. However, there is density in weaker topologies. In addition, we have already shown a class of operators that are transitive throughout Banach's space and that their perturbates have large transitive sets. The purpose of this master's thesis is to familiarize the candidate with the techniques used in this area and let him to discover open problems in this theory. (AU)