Dilations for systems of imprimitivity acting on Banach spaces
Abbreviated Journal Title
J. Funct. Anal.
Dilation; System of imprimitivity; Banach space; Projective isometric; representation; Operator-valued measure; Frame; FRAME REPRESENTATIONS; Mathematics
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. (C) 2014 Elsevier Inc. All rights reserved.
Journal of Functional Analysis
"Dilations for systems of imprimitivity acting on Banach spaces" (2014). Faculty Bibliography 2010s. 5409.