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中文摘要：
讨论了Hilbert C^＊-模上的有界线性算子网的严格收敛性与范数收敛性、强收敛性、弱收敛性之间的关系,证明了：严格收敛的算子网{Tλ}λ∈Λ的伴随算子网{Tλ^＊}λ∈Λ也是严格收敛的;严格收敛性是保持加法和数乘运算的;两个严格收敛算子网之积仍是严格收敛的;严格收敛的算子网一定是强收敛的.
英文摘要：
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 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.
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