Spaces of holomorphic functions defined on Banach spaces and the Michael’s problem

• Grant number: 14/50536-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2015
• End date: February 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jorge Tulio Mujica Ascui
• Grantee: Vinícius Vieira Fávaro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project is inserted in the area of functional analysis, and it is turned to the study of homomorphy and algebra of functions, as we describe below: (I) we intend to contribute meaningfully for the study of convolution equations, operators on spaces of entire functions defined between Banach spaces, mainly in two senses. First, we will seek new existence and approximation results for convolution equations; and second, we will develop the theory of hypercyclicity of convolution operators. (II) we will study some algebras of holomorphic functions and we will use this to attempt to solve the Michael's problem (if every homomorphism on a commutative Fréchet algebra is continuous). Several authors has been reduced the Michael's problem for algebras of entire functions. Besides, a better understanding of these algebras it will enable, for example, to study hypercyclicity results for them. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FAVARO, VINICIUS V.; MUJICA, JORGE. HYPERCYCLIC CONVOLUTION OPERATORS ON SPACES OF ENTIRE FUNCTIONS. JOURNAL OF OPERATOR THEORY, v. 76, n. 1, p. 141-158, SUM 2016. (14/50536-7)

FAVARO, VINICIUS V.; PELLEGRINO, DANIEL. Duality results in Banach and quasi-Banach spaces of homogeneous polynomials and application. STUDIA MATHEMATICA, v. 240, n. 2, p. 123-145, 2018. (14/50536-7)