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The Parallel Sum for Adjointable Operators on Hilbert C*-Modules
Wei LUO, Chuan Ning SONG, Qing Xiang XU
Acta Mathematica Sinica, Chinese Series ›› 2019, Vol. 62 ›› Issue (4) : 541-552.
PDF(532 KB)
PDF(532 KB)
The Parallel Sum for Adjointable Operators on Hilbert C*-Modules
The parallel sum for adjointable 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, B ∈ L (H) such that the operator equation A1/2=(A + B)1/2X, X ∈ L (H) has no solution, where L (H) denotes the set of all adjointable operators on H.
Hilbert C*-module / Moore-Penrose inverse / parallel sum {{custom_keyword}} /
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