The works on linear dynamics in the last two decades show that many, even quite natural, linear dynamical systems exhibit wild behavior. Linear chaos and hypercyclicity have been at the crossroads of several areas of mathematics. More recently, fascinating new connections have started to be explored: operators on spaces of analytic functions, semigroups and applications to partial differential equations, complex dynamics, and Ergodic theory.

Related aspects of functional analysis are the study of linear operators on Banach spaces by using geometric, topological, and algebraic techniques, the works on the geometry of Banach spaces and Banach algebras, and the study of the geometry of a Banach space via the behavior of some of its operators.

In recent years, some aspects of the theory of infinite dimensional complex analysis have attracted the attention of several researchers: one in the general field of Banach and Frechet algebras and Banach spaces of polynomial and holomorphic functions, and another in a deep connection with the theory of one and several complex variables as Dirichlet series in one variable, Bohr radii in several variables, Bohnenblust-Hille constants, Sidon constants, domains of convergence, and so forth.

With the present high activity in these fields, with the appearance of many young researchers, after the solution of several open problems, and in view of some major remaining challenges, we believe that it is the ideal time for bringing together some of the main advances in a special issue. Potential topics include, but are not limited to:

• Linear dynamics of operators, Ergodic theory, and asymptotic behavior of semigroups of operators associated with linear PDEs
• Dynamics of polynomials on Banach and Frechet spaces
• Norm-attaining operators, numerical range of operators, and Daugavet and related properties
• Isometries on Banach spaces
• Nonlinear analysis in infinite dimensions: Dirichlet series and power series in infinite dimensional spaces

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