Structure Theorem for Commutators of Operators
نویسندگان
چکیده
If 3C is a separable (complex) Hubert space, and A is a (bounded, linear) operator on 3C, then A is a commutator if there exist operators B and C on 3C such that 4 = BCCB. I t was shown by Wintner [8] and also by Wielandt [7] that no nonzero scalar multiple of the identity operator I on 3C is a commutator, and this was improved by Halmos [5] who showed that no operator of the form X / + C is a commutator, where XT^O and C is a compact operator. The purpose of this note is to announce the following theorem and give some indication of its proof. Details of the results described below will appear elsewhere [2].
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