Complementary bounds for the numerical and spectral radii
Fuad Kıttaneh, Hamid Reza Moradi, Mohammad Sababheh · Quaestiones Mathematicae · 2025
Let denote the C* –algebra of all bounded linear operators on a Hilbert space . Among other results, we show that if are nonzero, thenwhere denote the operator norm and the numerical radius, respectively. This provides a significant improvement and reverse of the known boundTo achieve this, we treat the triangle inequality and a well-known identity for the numerical radius of an operator matrix. Using the same technique, we then present an inequality for the spectral radius of the sum of two operators.The results obtained are compared with those of the existing literature. Many other results are shown as refinements or reverses of other known facts about the numerical radius and the usual operator norm.