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Hilbert modules characterization for weak hyperrigid operator systems

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Abstract

A characterization of weak hyperrigidity for certain separable operator systems in \(W^*\)-algebras in terms of the orthogonality properties of Hilbert modules over operator algebras is established.

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References

  1. Arveson, W.B. 1969. Subalgebras of \(C^{*}\)-algebras. Acta Mathematica 123: 141–224.

    Article  MathSciNet  Google Scholar 

  2. Arveson, W.B. 1972. Subalgebras of \(C^*\)-algebras II. Acta Mathematica 128: 271–308.

    Article  MathSciNet  Google Scholar 

  3. Arveson, W.B. 2011. The noncommutative Choquet boundary II: Hyperrigidity. Israel Journal of Mathematics 184: 349–385.

    Article  MathSciNet  Google Scholar 

  4. Korovkin, P.P. 1960. Linear operators and approximation theory. Delhi: Hindustan.

    Google Scholar 

  5. Muhly, P., and B. Solel. 1995. Hilbert modules over operator algebras, Mem. Amer. Math. Soc., vol. 117. Providence: Amer. Math. Soc.

  6. Muhly, P., and B. Solel. 1998. An algebraic characterization of boundary representations. In Nonselfadjoint operator algebras, operator theory, and related topics, Oper. Theory Adv. Appl., vol. 104, 189–196. Basel: Birkhauser.

  7. Limaye, B.V., and M.N.N. Namboodiri. 1984. Weak Korovkin approximation by completely positive linear maps on \(B(H)\). Journal of Approximation Theory 42 (3): 201–211.

    Article  MathSciNet  Google Scholar 

  8. Namboodiri, M.N.N. 2012. Geometric theory of weak Korovkin sets. Operators and Matrices 6 (2): 271–278.

    Article  MathSciNet  Google Scholar 

  9. Namboodiri, M.N.N., S. Pramod, P. Shankar, and A.K. Vijayarajan. 2018. Quasi hyperrigidity and weak peak points for non-commutative operator systems. Proceedings of the Indian Academy of Sciences: Mathematical Sciences 128 (5): 66.

    MathSciNet  MATH  Google Scholar 

  10. Sarason, D. 1965. On spectral sets having connected complement. Acta Scientiarum Mathematicarum (Szeged) 2 (6): 289–299.

    MathSciNet  MATH  Google Scholar 

  11. Saskin, Y.A. 1966. Korovkin systems in spaces of continuous functions. American Mathematical Society Translations 54 (2): 125–144.

    Article  Google Scholar 

  12. Shankar, P., and A.K. Vijayarajan. 2017. Hyperrigid operator systems and Hilbert modules. Annals of Functional Analysis 8 (1): 133–141.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The first author thanks the National Board for Higher Mathematics (NBHM), India, for providing financial support to carry his research.

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Correspondence to P. Shankar.

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Shankar, P., Vijayarajan, A.K. Hilbert modules characterization for weak hyperrigid operator systems. J Anal 28, 905–912 (2020). https://doi.org/10.1007/s41478-020-00220-6

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  • DOI: https://doi.org/10.1007/s41478-020-00220-6

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