Skip to main content
SpringerLink
Log in

On the tensor products of operators

  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

In this paper some necessary and sufficient conditions are obtained for a operator tensor product\(\sum\limits_k {A_{1k} \otimes A_{2k} \otimes \cdot \cdot \cdot \otimes A_{nk} } \) to be zero, compact, normal, hyponormal, subnormal, essential normal,k-quasihyponormal, etc.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Li Shao-kuan & Yan Shao-zong,On the Putnam-Fuglede theorem (Chinese), Kexue Tongbao,11 (1985), 810–813.

    MathSciNet  Google Scholar 

  2. Yan Shao-zong & Zhu Jian-zhong, On operator equation λA 2+μA *2=αA * A+βAA * (Chinese), Science in China,A11 (1987), 1139–1146.

    Google Scholar 

  3. Du Hong-ke & Hou Jin-chuan,The equivalence of three forms of the Putnam-Fuglede theorem, and some related results (Chinese), Chinese Ann. Math.,A6 (1985), 187–196.

    MathSciNet  Google Scholar 

  4. Hou Jin-chuan & Wang Yong-ming,k-quasihyponormal operators on the Hilbert-Schmidt class (Chinese), J. Math. Res. Exp.,9 (1989), 57–62.

    MathSciNet  MATH  Google Scholar 

  5. Li Gang,Quasinormality of the elementary operators on C 2 (H) (Chinese), Acta Math. Sinica,32 (1989), 219–224.

    MathSciNet  MATH  Google Scholar 

  6. Magajna, B.,On subnormality of generalized derivations and tensor products, Bull. Aust. Math. Soc.,31 (1985), 235–243.

    Article  MathSciNet  MATH  Google Scholar 

  7. Hou Jin-chuan,Solution of operator equations and tensor products, J. Math. Res. Exp.,12 (1992), 479–486.

    MATH  Google Scholar 

  8. Kadison, R.V. & Ringrose, J.R.,Fundamentals of the theory of operator algebras, Vol. I, Academic Press, New York, 1983.

    MATH  Google Scholar 

  9. Conway, J. B. & Szymanski, W.,Linear combinations of hyponormal operators, Rocky Mountain J. Math.,18 (1988), 695–705.

    Article  MathSciNet  MATH  Google Scholar 

  10. Arveson, W.,An invitation to C *-algebras, Springer-verlag, New York, 1976.

    MATH  Google Scholar 

  11. Halmos, P.R.,A Hilbert space problem book, Amer. Book Co., New York, 1967.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Math, Shanxi Teachers Univ., Linfen, China

    Hou Jinchuan

Authors
  1. Hou Jinchuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by Natural Science Fundation of Shanxi Province.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jinchuan, H. On the tensor products of operators. Acta Mathematica Sinica 9, 195–202 (1993). https://doi.org/10.1007/BF02560050

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02560050

Keywords

Search

Navigation