Annals of Functional Analysis

Hyperrigid operator systems and Hilbert modules

P. Shankar and A. K. Vijayarajan

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It is shown that, for an operator algebra A, the operator system S=A+A in the C-algebra C(S), and any representation ρ of C(S) on a Hilbert space H, the restriction ρ|S has a unique extension property if and only if the Hilbert module H over A is both orthogonally projective and orthogonally injective. As a corollary we deduce that, when S is separable, the hyperrigidity of S is equivalent to the Hilbert modules over A being both orthogonally projective and orthogonally injective.

Article information

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

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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]

operator system Hilbert module hyperrigidity unique extension property


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.

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