Geodesic
On the Chordal Transform of Hilbert Space Operators
Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 275-284

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Let B(H) denote the C*-algebra of all bounded linear operators on a separable Hilbert space H. For A,B∈B(H), the chordal transform f_(A,B), as an operator on B(H), is defined by {f_(A,B)(X)=(\vert A^*\vert ^2+I)^(-1/2){\delta_(A,B)(X)(\vert B\vert ^2+I)^(-1/2)}, where {\delta_(A,B)} is the generalized derivation defined on B(H) by {\delta _(A,B)(X)=AX-XB}. Orthogonality of the range and the kernel of f_(A,B), with respect to the unitarily invariant norms \vert \vert \vert .\vert \vert \vert , are discussed. It is shown that if A, B are self-adjoint, then {\vert \vert \vert f_(A,B)(X)\vert \vert \vert \le \vert \vert \vert X\vert \vert \vert for all X. Related norm inequalities comparing f_(A,B) and {\delta _(A,B) are also given. 
Hirzallah, Omar; Kittaneh, Fuad. On the Chordal Transform of Hilbert Space Operators. Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 275-284. doi: 10.1017/S0017089502020086
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     title = {On the {Chordal} {Transform} of {Hilbert} {Space} {Operators}},
     journal = {Glasgow mathematical journal},
     pages = {275--284},
     year = {2002},
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