Reverse Triangle Inequality in Hilbert $C*$-Modules

摘要

We prove several versions of the reverse triangle inequality in Hilbert -modules. We show that if are vectors in a Hilbert module over a -algebra with unit 1 such that eq j leq m)$"> and , and and satisfy olimits langle r... ...^2 Vert x_jVert leq mathop{m Im}olimits langle ho_ke_k,x_j rangle ,$"> then and the equality holds if and only if