The dynamics of linear operators is a young and rapidly evolving branch of functional analysis. In this book, which focuses on hypercyclicity and supercyclicity, the authors assemble the wide body of theory that has received much attention over the last fifteen years and present it for the first time in book form. Selected topics include various kinds of 'existence theorems', the role of connectedness in hypercyclicity, linear dynamics and ergodic theory, frequently hypercyclic and chaotic operators, hypercyclic subspaces, the angle criterion, universality of the Riemann zeta function, and an introduction to operators without non-trivial invariant subspaces. Many original results are included, along with important simplifications of proofs from the existing research literature, making this an invaluable guide for students of the subject. This book will be useful for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.

Given a Polish topology τ on B1pXq, the set of all contraction operators on X " ℓp, 1 ď p ă 8 or X " c0, we prove several results related to the following question: does a typical T P B1pXq in the Baire Category sense has a non-trivial invariant subspace? In other words, is there a dense G δ set G Ď pB1pXq, τ q such that every T P G has a non-trivial invariant subspace? We mostly focus on the Strong Operator Topology and the StrongO perator Topology.

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By a recent result of M. De La Rosa and C. Read, there exist hypercyclic Banach space operators which do not satisfy the Hypercyclicity Criterion. In the present paper, we prove that such operators can be constructed on a large class of Banach spaces, including c 0 (N) or p (N).