Dilations for systems of imprimitivity acting on Banach spaces Academic Article

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.

authors

• Larson, David

published proceedings

• JOURNAL OF FUNCTIONAL ANALYSIS

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

• January 2014

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

keywords

• Banach Space
• Dilation
• Frame
• Operator-valued Measure
• Projective Isometric Representation
• System Of Imprimitivity

Digital Object Identifier (DOI)

• 10.1016/j.jfa.2014.02.040

start page

• 6914

end page

• 6937

volume

• 266

issue

• 12