Abstract
For A in the algebra B(H) of bounded linear operators on a separable complex Hilbert space H the corresponding inner derivation δA on B(H) is given by δA(X)=AX−XA. If dim H<∞ then (*) B(H)=R(δA)⊗{A*}′ is the orthogonal direct sum of the range of δA and the commutant of A* with respect to the inner product (X,Y)=trace (XY*). This simple formula suggests that R(δA) is just as natural a subspace of B(H) as its orthogonal complement {A*}′ and hence is worthy of its own investigation.
Research supported in part by a grant from the National Science Foundation
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Williams, J.P. (1981). Derivation Ranges: Open Problems. In: Apostol, C., Douglas, R.G., Nagy, B.S., Voiculescu, D., Arsene, G. (eds) Topics in Modern Operator Theory. Operator Theory: Advances and Applications, vol 2. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5456-6_21
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DOI: https://doi.org/10.1007/978-3-0348-5456-6_21
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