Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T21:30:18.750Z Has data issue: false hasContentIssue false
  • English
  • Français

Reflexivity of the group of surjective isometries on some Banach spaces

Published online by Cambridge University Press:  20 January 2009

Lajos Molnár  and
Borut Zalar
Lajos Molnár
Affiliation:
Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O. Box 12, Hungary, E-mail address: [email protected]
Borut Zalar
Affiliation:
Department of Basic Sciences, Faculty of Civil Engineering, University of mariborSmetanova 17 62000 MariborSlovenija E-mail address: [email protected] or [email protected]
Rights & Permissions [Opens in a new window]

Extract

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.

In this paper we study the problem of algebraic reflexivity of the isometry group of some important Banach spaces. Because of the previous work in similar topics, our main interest lies in the von Neumann – Schatten p-classes of compact operators. The ideas developed there can be used in ℓp-spaces, Banach spaces of continuous functions and spin factors as well. Moreover, we attempt to attract the attention to this problem from general Banach spaces geometry view-point. This study, we believe, would provide nice geometrical results.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 17 - 36
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Arazy, J., The isometrics of Cp, Israel J. Math. 22 (1975), 247–256.CrossRefGoogle Scholar
2.Arveson, W. B., Continuous analogues of Fock spaces, Mem. Amer. Math. Soc. 80 (1989), 409.Google Scholar
3.Brešar, M., Characterization of derivations on some normed algebras with involution, J. Algebra 152 (1992), 454–462.CrossRefGoogle Scholar
4.Brešar, M. and Šemrl, P., Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483–196.CrossRefGoogle Scholar
5.Brešar, M. and Šemrl, P., On local automorphisms and mappings that preserve idempotents, Studia Math. 113 (1995), 101–108.CrossRefGoogle Scholar
6.Dang, T., Friedman, Y. and Russo, B., Affine geometric proofs of the Banach Stone theorems of Kadison and Kaup, Rocky Mountain J. Math. 20 (1990), 409–428.Google Scholar
7.Erdos, J. A., A simple proof of Arazy's theorem, Proc. Edinburgh Math. Soc. 37 (1994), 239–242.CrossRefGoogle Scholar
8.Kadison, R. V., Local derivations, J. Algebra 130 (1990), 494–509.CrossRefGoogle Scholar
9.Kaup, W., A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983), 503–529.Google Scholar
10.Larson, D. R., Reflexivity, algebraic reflexivity and linear interpolation, Amer. J. Math. 110 (1988), 283–299.CrossRefGoogle Scholar
11.Larson, D. R. and Sourour, A. R., Local derivations and local automorphisms of B(X) (Proc. Sympos. Pure Math. 51, Part 2, Providence, Rhode Island 1990), 187–194.CrossRefGoogle Scholar
12.Loginov, A. J. and Shul'man, V. S., Hereditary and intermediate reflexivity of W*-algebras, Izv. Akad. Nauk SSSR 39 (1975), 1260–1273; English transl. in USSR-Isv. 9 (1975), 1189–1201.Google Scholar
13.Molnár, L., The set of automorphisms of B(H) is topologically reflexive in B(B(H)), preprint.Google Scholar
14.Molnár, L. and Zalar, B., On automatic surjectivity of Jordan homomorphisms, Acta Sci. Math. (Szeged) 61 (1995), 413–424.Google Scholar
15.Royden, H. L., Real Analysis (Macmillan, New York, 1963).Google Scholar
16.Russo, B. and Dye, H. A., A note on unitary operators in C*-algebras, Duke Math. J. 33 (1966), 413–416.Google Scholar
17.Shul'man, V. S., Operators preserving ideals in C*-algebras, Studia Math. 109 (1994), 67–72.CrossRefGoogle Scholar
18.Sourour, A. R., Isometries of norm ideals of compact operators, J. Funct. Anal. 43 (1981), 69–77.Google Scholar
19.Størmer, E., On the Jordan structure of C*-algebras, Trans. Amer. Math. Soc. 120 (1965), 438–447.Google Scholar