Best approximation by diagonal compact operators - Bottazzi, Tamara Paula (2013)
We study the existence and characterization properties of compact Hermitian operators C on a Hilbert space H such that the norm of C is less or equal to that of C + D , for all the real and compact diagonals D in a fixed base of H (in the operator norm). We also exhibit a positive trace class operator that fails to attain the minimum in a compact diagonal.