Glasgow Mathematical Journal

Research Article

BANACH SPACES WITH SEPARABLE DUALS SUPPORT DUAL HYPERCYCLIC OPERATORS

HÉCTOR N. SALASa1

a1 Department of Mathematics, University of Puerto Rico, Mayagüez, Puerto Rico 00681 e-mail: salas@math.uprm.edu

Abstract

Let E be a Banach space such that its dual E* is separable. We show that there exists a hypercyclic bounded operator T on E such that its adjoint T* is also hypercyclic on E*. We also exhibit a new kind of dual hypercyclic operator. Thus answers affirmatively two of the questions raised by Henrik Petersson in a recent paper.

(Received August 04 2006)

(Revised January 03 2007)

(Revised March 13 2007)

(Accepted March 19 2007)

Key Words:

  • Primary 47A16;
  • 47A05;
  • Secondary 47B37