The relationships between the strict convergence and norm convergence, strong convergence as well as weak convergence of a net of bounded linear operators on a Hilbert C*-module are discussed. Following conclusions are proved: if a net {Tλ}λ∈Λ of bounded linear operators is strictly convergent, then the adjoint net {T*λ}λ∈Λ is also strictly convergent; the strict convergence of a net of bounded linear operators preserves the addition and multiplication of operations; a product of two strictly convergent nets of bounded linear operators is strictly convergent; a strictly convergent net of bounded linear operators is strongly convergent.

Hilbert C*-module; C*-algebra; strict convergence; strong convergence; weak convergence; norm convergence