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Frame-Less Hilbert C\(^*\)-modules II

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Abstract

We show that if A is a non-unital \(C^*\)-algebra of compact operators, which is \( *\)-isomorphic to \(\oplus _{i \in I} K(H_{i})\), where I is an arbitrary index set and for every \( i \in I \), \(H_{i} \) is a separable Hilbert space, then there exists a Hilbert \(A_1\)-module admitting no frames, where \(A_1\) is the unitization of A.

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References

  1. Arveson, W.: An Invitation to \(C^*\)-algebras. Springer, New York (1976)

    Book  Google Scholar 

  2. Amini, M., Asadi, M.B., Elliott, G.A., Khosravi, F.: Frames in Hilbert \(C^*\)-modules and Morita equivalent \(C^*\)-algebras. Glasg. Math. J. 59, 1–10 (2017)

    Article  MathSciNet  Google Scholar 

  3. Asadi, M.B., Frank, M., Hassanpour-Yakhdani, Z.: frame-less Hilbert \(C^{\ast } \)-modules. Glasg. Math. J. 61, 25–31 (2019)

    Article  MathSciNet  Google Scholar 

  4. Elliott, G.A., Kawamura, K.: A Hilbert bundle characterization of Hilbert \(C^*\)-modules. Trans. Am. Math. Soc. 360, 4841–4862 (2008)

    Article  MathSciNet  Google Scholar 

  5. Frank, M., Larson, D.R.: Frames in Hilbert \( C^{*} \)-modules and \( C^{*} \)-algebras. J. Oper. Theory 48, 273–314 (2000)

    MathSciNet  MATH  Google Scholar 

  6. Li, H.: A Hilbert \(C^*\)-module admitting no frames. Bull. Lond. Math. Soc. 42, 388–394 (2010)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This research was supported by the Iran National Science Foundation (INSF) [research Project No. 97006005].

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    Mohammad B. Asadi & Zahra Hassanpour-Yakhdani

  2. Fakultät IMN, Hochschule für Technik, Wirtschaft und Kultur (HTWK) Leipzig, PF 301166, 04251, Leipzig, Germany

    Michael Frank

Authors
  1. Mohammad B. Asadi
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  2. Michael Frank
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  3. Zahra Hassanpour-Yakhdani
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Correspondence to Mohammad B. Asadi.

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Communicated by Daniel Aron Alpay.

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This article is part of the topical collection “Infinite-dimensional Analysis and Non-commutative Theory (Marek Bozejko, Palle Jorgensen and Yuri Kondratiev”.

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Asadi, M.B., Frank, M. & Hassanpour-Yakhdani, Z. Frame-Less Hilbert C\(^*\)-modules II. Complex Anal. Oper. Theory 14, 32 (2020). https://doi.org/10.1007/s11785-020-00990-8

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  • DOI: https://doi.org/10.1007/s11785-020-00990-8

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