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

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

MathSciNet review:
975661

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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 a Hilbert space*, Proc. Amer. Math. Soc.**84**(1982), 516-520. MR**643740 (84g:47039)****[2]**C. K. Fong and H. Radjavi,*On ideals and Lie ideals of compact operators*, Math. Ann. B**262**. H 1 (1983), 23-28. MR**690004 (84d:47059)****[3]**C. K. Fong and G. J. Murphy,*Ideals and Lie ideals of operators*, Acta Sci. Math. (Szeged)**51**(1987), 441-456. MR**940948 (89k:47067)****[4]**I. C. Gohberg and M. G. Krein,*Introduction to the theory of nonselfadjoint operators*, Transl. Amer. Math. Soc.,**18**, Providence, RI, 1969. MR**0246142 (39:7447)**

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

Article copyright:
© Copyright 1990
American Mathematical Society