On unitary invariant ideals in the algebra of compact operators

Author:
József V. Varga

Journal:
Proc. Amer. Math. Soc. **108** (1990), 789-794

MSC:
Primary 47D25

MathSciNet review:
975661

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Lie ideals are constructed, which are ideals in the algebra of compact operators but not ideals in the algebra of bounded operators, thus settling a question of C. K. Fong and H. Radjavi in the negative.

**[1]**C. K. Fong, C. R. Miers, and A. R. Sourour,*Lie and Jordan ideals of operators on Hilbert space*, Proc. Amer. Math. Soc.**84**(1982), no. 4, 516–520. MR**643740**, 10.1090/S0002-9939-1982-0643740-0**[2]**C. K. Fong and H. Radjavi,*On ideals and Lie ideals of compact operators*, Math. Ann.**262**(1983), no. 1, 23–28. MR**690004**, 10.1007/BF01474167**[3]**C. K. Fong and G. J. Murphy,*Ideals and Lie ideals of operators*, Acta Sci. Math. (Szeged)**51**(1987), no. 3-4, 441–456. MR**940948****[4]**I. C. Gohberg and M. G. Kreĭn,*Introduction to the theory of linear nonselfadjoint operators*, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR**0246142**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
47D25

Retrieve articles in all journals with MSC: 47D25

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-0975661-2

Article copyright:
© Copyright 1990
American Mathematical Society