Dilations for systems of imprimitivity acting on Banach spaces Academic Article uri icon

abstract

  • Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-known result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space. This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces. © 2014 Elsevier Inc.

altmetric score

  • 0.25

author list (cited authors)

  • Han, D., Larson, D. R., Liu, B., & Liu, R.

citation count

  • 5

complete list of authors

  • Han, Deguang||Larson, David R||Liu, Bei||Liu, Rui

publication date

  • June 2014