Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-23T13:34:15.115Z Has data issue: false hasContentIssue false
  • English
  • Français

n-Reflexivity for linear spaces of operators

Published online by Cambridge University Press:  18 May 2009

Kun Wook Choi
Kun Wook Choi
Affiliation:
Department of MathematicsCollege of National SciencesKyungpook National University, Tague, 702–702, S. Korea
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We discuss the relationship between the n-reflexivity of a linear sub-space S in B(H), property (A1/n), Class Co and strictly n-separating vectors. We also show that every algebraic operator with property (A2) is hyperreflexive.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998 , pp. 385 - 391
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

REFERENCES

1.Azoff, E. A., On finite rank operators and preannihilators, Mem. Amer. Math. Soc. 357 (1986).Google Scholar
2.Bercovici, H., Operator theory and arithmetic in H°°, (Amer. Math. Soc, 1988).CrossRefGoogle Scholar
3.Bercovici, H., Foias, C. and Sz-Nagy, B., Reflexive and hyperreflexive operators of class Co, Acta Sci. Math. (Szeged) 43 (1981), 5–13.Google Scholar
4.Bercovici, H., Foias, C. and Pearcy, C., Dual algebra with applications to invariant subspaces and dilation theory, CBMS Conf. Ser. in Math. No. 56 (Amer. Math. Soc, 1985).CrossRefGoogle Scholar
5.Bercovici, H., Kim, H. and Pearcy, C., On reflexivity of operators, J. Math. Anal. Appl. 126 (1987), 316–323.Google Scholar
6.Chevreau, B. and Esterle, J., Pettis'lemma and topological properties of dual algebras, Michigan Math. J. 34 (1987), 141–146.CrossRefGoogle Scholar
7.Choi, K., Jo, Y. and Jung, I., Dual operator algebras generated by a Jordan operator, Kyungpook Math. J. 34 (1994), 43–51.Google Scholar
8.Choi, K., Jung, I. and Kim, B., On weak dilation of a representation, Houston J. Math. 22 (1996), 341–355.Google Scholar
9.Ding, L., On strictly separating vectors and reflexivity, Integral Equations Operator Theory 19 (1994), 373–380.CrossRefGoogle Scholar
10.Ding, L., On a pattern of reflexivite operator spaces, Proc. Amer. Math. Soc, to appear.Google Scholar
11.Hadwin, D., Compression, graphs and hyperreflexivity, J. Fund. Anal., to appear.Google Scholar
12.Hadwin, D. and Nordgren, E., Reflexivity and direct sums, Ada Sci. Math. (Szeged) 55 (1991), 181–197.Google Scholar
13.Kraus, J. and Larson, D., Some applications of a technique for constructing reflexive operator algebras, J. Operator Theory 13 (1985), 227–236.Google Scholar
14.Loginov, A. I. and Shulman, V. S., On hereditary and intermediate reflexivity of w*-algebras, Izv. Akad. Nauk SSSR Ser. Math. 396 (1975), 1260–1273.Google Scholar
15.Sz-Nagy, B. and Foias, C., Harmonic analysis of operators on Hilbert space (North-Holland, 1970).Google Scholar
16.Takahashi, K., On the reflexivity of contractions with isometric parts, Ada Sci. Math. (Szeged) 53 (1989), 147–152.Google Scholar