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Rank-one operators in reflexive one-sidedA-submodules

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Abstract

In this paper, we first characterize reflexive one-sided A-submodulesU of a unital operator algebraA inB(H) completely. Furthermore we investigate the invariant subspace lattice LatR and the reflexive hull RefR, whereR is the submodule generated by rank-one operators inU; in particular, ifL is a subspace lattice, we obtain when the rank-one algebraR of AlgL is big enough to determined AlgL in the following senses: AlgL = Alg LatR and AlgL = RefR.

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References

  1. Bradley S, Finite rank operators in certain algebras,Can. Math. Bull. 42 (1999) 452–462

    MATH  MathSciNet  Google Scholar 

  2. Erdos J A, Operators of finite rank in nest algebras,J. London Math. Soc. 43 (1968) 391–397

    Article  MATH  MathSciNet  Google Scholar 

  3. Erdos J A and Power S C, Weakly closed ideals of nest algebras,J. Op. Theory 7 (1982) 219–235

    MATH  MathSciNet  Google Scholar 

  4. Han Deguang, OnA-submodules for reflexive operator algebras,Proc. Am. Math. Soc. 104 (1988) 1067–1070

    Article  MATH  Google Scholar 

  5. Kraus J and Larson D, Reflexivity and distance formulae,Proc. London Math. Soc. 53(3) (1986) 340–356

    Article  MATH  MathSciNet  Google Scholar 

  6. Lambrou M S, Approximants, commutants and double commutants in normed algebras,J. London Math. Soc. 25(2) (1982) 499–512

    Article  MATH  MathSciNet  Google Scholar 

  7. Laurie C and Longstaff W E, A note on rank-one operators in reflexive algebras,Proc. Am. Math. Soc. 89 (1983) 293–297

    Article  MathSciNet  Google Scholar 

  8. Longstaff W E, Strongly reflexive lattices,J. London Math. Soc. 11(2) (1975) 491–498

    Article  MATH  MathSciNet  Google Scholar 

  9. Longstaff W E, Operators of rank one in reflexive algebras,Can. J. Math. 28 (1976) 19–23

    MATH  MathSciNet  Google Scholar 

  10. Longstaff W E, Nation J B and Oreste Panaia, Abstract reflexive sublattices and completely distributive collapsibility,Bull. Austral. Math. Soc. 58 (1998) 245–260

    Article  MATH  MathSciNet  Google Scholar 

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  1. Department of Mathematics, Zhejiang University, 310 027, Hangzhou, People’s Republic of China

    Dong Zhe

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  1. Dong Zhe
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Correspondence to Dong Zhe.

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Zhe, D. Rank-one operators in reflexive one-sidedA-submodules. Proc. Indian Acad. Sci. (Math. Sci.) 114, 55–63 (2004). https://doi.org/10.1007/BF02829671

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  • DOI: https://doi.org/10.1007/BF02829671

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