Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 8, Number 1 (2017), 133-141.
Hyperrigid operator systems and Hilbert modules
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.
Ann. Funct. Anal., Volume 8, Number 1 (2017), 133-141.
Received: 17 February 2016
Accepted: 1 August 2016
First available in Project Euclid: 12 November 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46L07: Operator spaces and completely bounded maps [See also 47L25]
Secondary: 46L52: Noncommutative function spaces 46L89: Other "noncommutative" mathematics based on C-algebra theory [See also 58B32, 58B34, 58J22]
Shankar, P.; Vijayarajan, A. K. Hyperrigid operator systems and Hilbert modules. Ann. Funct. Anal. 8 (2017), no. 1, 133--141. doi:10.1215/20088752-3773182. https://projecteuclid.org/euclid.afa/1478919627