J. ALBERTO CONEJERO
Disjointness has been recently introduced in linear dynamics independently by
Bernal-Gonz´alez [1] and B`es and Peris [2], inpsired by Furstenberg’s notion of disjointness
[4]. It has been considered by hypercyclicity (transitivity), mixing, weakly
mixing, and blow-up/collapse properties, providing analysis of these phenomena
for weighted shift operators. We provide a characterization of d-chaos for bilateral
weighted shifts and powers of bilateral weighted shifts operators in terms of their
weight sequences.
This is part of a joint work with C.C. Chen, M. Kostic, and M. Murillo-Arcila.
This research is supported by MEC Project: MTM2016-75963-P.
References
[1] L. Bernal-Gonz´alez. Disjoint hypercyclic operators. Studia Math., 182(2):113–131, 2007.
[2] J. B`es and A. Peris. Disjointness in hypercyclicity. J. Math. Anal. Appl., 336(1):297–315,
2007.
[3] C.C. Chen, J.A. Conejero, M. Kostic and M. Murillo-Arcila. Disjoint weighted shifts. Preprint,
2017.
[4] H. Furstenberg. Disjointness in ergodic theory, minimal sets, and a problem in Diophantine
approximation. Math. Systems Theory, 1:1–49, 1967.
Instituto de Matematica Pura y Aplicada. Universitat Politécnica de Valencia
E-mail address: aconejero@upv.es
Fourth Summer School in Complex Analysis and Operator Theory
