کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4590479 | 1334963 | 2014 | 24 صفحه PDF | دانلود رایگان |
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.
Journal: Journal of Functional Analysis - Volume 266, Issue 12, 15 June 2014, Pages 6914–6937