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تسجيل مستخدم جديدThe parallel sum for adjointable operators on Hilbert $C^*$-modules
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The parallel sum for adjoinable operators on Hilbert $C^*$-modules is introduced and studied. Some results known for matrices and bounded linear operators on Hilbert spaces are generalized to the case of adjointable operators on Hilbert $C^*$-modules. It is shown that there exist a Hilbert $C^*$-module $H$ and two positive operators $A, Binmathcal{L}(H)$ such that the operator equation $A^{1/2}=(A+B)^{1/2}X, Xin cal{L}(H)$ has no solution, where $mathcal{L}(H)$ denotes the set of all adjointable operators on $H$.
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