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摘要
Grosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N-linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Frechet space supports supercyclic N-linear operators, for each N %26gt;= 2. Indeed, the nonnormable spaces of entire functions and the countable product of lines support N-linear operators with residual sets of hypercyclic vectors, for N = 2.
- 出版日期2014
