A New Seminorm for d-Tuples of A-Bounded Operators and Their Applications

The aim of this paper was to introduce and investigate a new seminorm operator tuples on complex Hilbert space H when an additional semi-inner product structure defined by positive (semi-definite) A is considered. We prove the equality between well-known A-joint in case A-doubly-commuting A-hyponormal operators. This study extension result [Results Math 75, 93(2020)] allows us show that following equalities rA(T)=ωA(T)=∥T∥A hold for every d-tuple operators T=(T1,…,Td). Here, rA(T),∥T∥A, ωA(T) denote spectral radius, seminorm, numerical radius T, respectively.