Abstract
It is shown that, for an operator algebra , the operator system in the -algebra , and any representation of on a Hilbert space , the restriction has a unique extension property if and only if the Hilbert module over is both orthogonally projective and orthogonally injective. As a corollary we deduce that, when is separable, the hyperrigidity of is equivalent to the Hilbert modules over being both orthogonally projective and orthogonally injective.
Citation
P. Shankar. A. K. Vijayarajan. "Hyperrigid operator systems and Hilbert modules." Ann. Funct. Anal. 8 (1) 133 - 141, February 2017. https://doi.org/10.1215/20088752-3773182
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