On Jordan all-derivable points of \(\mathcal B(\mathcal H)\)
Let \(H\) be an infinite-dimensional Hilbert space. It is shown that a linear map \(\delta:B(H)\to B(H)\) satisfying \(\delta(A)A + A\delta(A) = A\delta(I)A\) whenever \(A^2 =0\) is a generalized derivation. Similarly, a linear map \(\delta:B(H)\to B(H)\) is a derivation provided that \(\delta(I) = \delta(A)A + A\delta(A)\) whenever \(A^2=I\) (here, \(H\) need not be infinite-dimensional).
scientific article; zbMATH DE number 5505603