• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.363-372
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• 2010

In this paper, we introduce and study the generalized inverse $A^{(1,2)}_{T,S}$ with the prescribed range T and null space S of an adjointable operator A from one Hilbert $C^*$-module to another, and get some analogous results known for finite matrices over the complex field or associated rings, and the Hilbert space operators.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.691-706
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• 2020

Necessary and sufficient conditions are provided under which the weighted Moore-Penrose inverse A^†_MN exists, where A is an adjointable operator between Hilbert C^⁎-modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore-Penrose inverses A^†_MN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore-Penrose inverse is also provided.

• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.31-39
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• 2011

Stone's theorem states that "A bounded linear operator A is infinitesimal generator of a $C_0$-group of unitary operators on a Hilbert space H if and only if iA is self adjoint". In this paper we establish a generalization of Stone's theorem in the framework of Hilbert $C^*$-modules.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.367-373
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• 2007

For a unital *-subalgebra of the space $\mathcal{L}^a(X)$ of all adjointable maps on a Hilbert $\mathcal{B}$-module X with a $C^*$-algebra $\mathcal{B}$, we study unitary operator (in such algebra)-valued multiplier ${\sigma}$ on a normal, generating subsemigroup S of a group G with its extension to G. A dilation of a projective isometric ${\sigma}$-representation of S is established as a projective unitary ${\rho}$-representation of G for a suitable unitary operator (in some algebra)-valued multiplier ${\rho}$ associated with the multiplier ${\sigma}$ which is explicitly constructed.