Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators.
The Shannon inequality asserts that if \(\{a_1,\dots, a_n\}\) and \(\{b_1,\dots, b_n\}\) are two probability vectors, then \(\sum^n_{j=1} a_j\log{b_j\over a_j}\leq 0\). The authors give parametric extensions of the Shannon inequality and its reverse for Hilbert space operators.
scientific article; zbMATH DE number 2069728