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Necessary and sufficient conditions are provided under which the weighted Moore--Penrose inverse $A^\dag_{MN}$ 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 $A^\dag_{MN}$ is clarified when $A$ is fixed, whereas $M$ and $N$ are variable. Perturbation analysis for the weighted Moore--Penrose inverse is also provided.
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참고문헌 (15)
참고문헌 신청
Enrico Boasso / 2013 / Weighted Moore-Penrose invertible and weighted EP Banach algebra elements / 대한수학회지 50(6):1349~1367
G. Corach / 2005 / Weighted generalized inverses, oblique projections, and least-squares problems / Numer. Funct. Anal. Optim. 26(6):659~673
A. Hernandez / 2013 / On a partial order dened by the weighted Moore-Penrose inverse / Appl. Math. Comput 219(14):7310~7318
K. Kamaraj / 2005 / Moore-Penrose inverse in an indefinite inner product space / Journal of Applied Mathematics and Informatics 19(1-2):297~310
J. J. Koliha / 2001 / Continuity and dierentiability of the Moore-Penrose inverse in C-algebras / Math. Scand 88(1):154~160
G. Corach / 2005 / Weighted generalized inverses, oblique projections, and least-squares problems / Numer. Funct. Anal. Optim. 26(6):659~673
A. Hernandez / 2013 / On a partial order dened by the weighted Moore-Penrose inverse / Appl. Math. Comput 219(14):7310~7318
K. Kamaraj / 2005 / Moore-Penrose inverse in an indefinite inner product space / Journal of Applied Mathematics and Informatics 19(1-2):297~310
J. J. Koliha / 2001 / Continuity and dierentiability of the Moore-Penrose inverse in C-algebras / Math. Scand 88(1):154~160
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