Somewhere Dense Orbit that is not Dense on a Complex Hilbert Space

Abstract

Abstract In this paper, we present the existence of n-tuple of operators on complex Hilbert space that has a somewhere dense orbit and is not dense. We give the solution to the question stated in [11]: “Is there n-tuple of operators on a complex Hilbert space that has a somewhere dense orbit that is not dense?” We do so by extending the results due to Feldman [11] and Leòn-Saavedra [12] to complex Hilbert space. Further illustrative examples of somewhere dense orbits are given to support the results.