2021/01/12 by Zamani, Ali
#46B20 #46L05 #47A12 #47A30 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2101.04396
Utilizing the linking algebra of a Hilbert C^*-module (\mathscrV, ‖ ⋅ ‖), we introduce Ω(x) as a definition of numerical radius for an element x∈\mathscrV and then show that Ω(⋅) is a norm on \mathscrV such that (1)/(2)‖x‖ ≤ Ω(x) ≤ ‖x‖. In addition, we obtain an equivalent condition for Ω(x) = (1)/(2)‖x‖. Moreover, we present a refinement of the triangle inequality for the norm Ω(⋅). Some other related results are also discussed.