The Daugavet Equation for polynomials and holomorphic mappings

• Grant number: 09/00016-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Effective date (Start): April 01, 2009
• Effective date (End): February 28, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jorge Tulio Mujica Ascui
• Grantee: Elisa Regina dos Santos
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 06/02378-7 - Infinite Dimensional Analysis, AP.TEM

Abstract

The equation ||I + T|| = 1 + ||T||, where T is an operator on a Banach space, is called Daugavet equation. Although this is a purely isometric property, it can be used to obtain some topological conclusions regarding Banach spaces.The Daugavet equation has been studied by many authors in various contexts along the 45 last years. Recently Y. S. Choi, D. García, M. Maestre and M. Martín studied the equation for polynomials in spaces of continuous functions in the following paper "The Daugavet equation for polynomials".In this work, we intend to extend the results founded in the cited paper and the results presented by V. M. Kadets, R. V. Shvidkoy, G. G. Sirotkin and D.Werner in the paper called "Banach spaces with the Daugavet property". Furthermore, the Daugavet equation for holomorphic mappings will be also studied.

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)

SANTOS, ELISA R.. An alternative polynomial Daugavet property. STUDIA MATHEMATICA, v. 224, n. 3, p. 265-276, 2014. (09/00016-9)