## Which operators are the self-commutators of compact operators?(English)Zbl 0442.47024

### MSC:

 47B47 Commutators, derivations, elementary operators, etc. 47B06 Riesz operators; eigenvalue distributions; approximation numbers, $$s$$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators

### Keywords:

self-commutator; compact operator; trace
Full Text:

### References:

 [1] Arlen Brown, P. R. Halmos, and Carl Pearcy, Commutators of operators on Hilbert space, Canad. J. Math. 17 (1965), 695 – 708. · Zbl 0131.12401 [2] P. Fillmore, C. K. Fong and A. Sourour, Real parts of quasi-nilpotent operators, Proc. Edinburgh Math. Soc. (to appear). · Zbl 0412.47009 [3] 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. · Zbl 0181.13504 [4] C. Pearcy, Some unsolved problems in operator theory, preprint, 1972. [5] Carl Pearcy and David Topping, On commutators in ideals of compact operators, Michigan Math. J. 18 (1971), 247 – 252. · Zbl 0226.46066 [6] Heydar Radjavi, Structure of \?*\?-\?\?*, J. Math. Mech. 16 (1966), 19 – 26. · Zbl 0143.16201 [7] Joseph G. Stampfli, Hyponormal operators, Pacific J. Math. 12 (1962), 1453 – 1458. · Zbl 0129.08701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.