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Weighted gDMP inverse of operators between Hilbert spaces

Dijana Mosic
대한수학회 (The Korean Mathematical Society)|2018.07|대한수학회보 (Bulletin of the KMS)|제55권 제4호|pp. 1263-1271

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참고문헌

키워드

Hilbert spaceMoore-Penrose inverseDMP inverseWg-Drazin inverse
주제분류수학

초록

We introduce new generalized inverses (named the WgDMP inverse and dual WgDMP inverse) for a bounded linear operator between two Hilbert spaces, using its Wg-Drazin inverse and its Moore-Penrose inverse. Some new properties of WgDMP inverse and dual WgDMP inverse are obtained and some known results are generalized.

Abstract

We introduce new generalized inverses (named the WgDMP inverse and dual WgDMP inverse) for a bounded linear operator between two Hilbert spaces, using its Wg-Drazin inverse and its Moore-Penrose inverse. Some new properties of WgDMP inverse and dual WgDMP inverse are obtained and some known results are generalized.

참고문헌 (12)

  1. O. M. Baksalary, "Core inverse of matrices", Linear Multilinear Algebra, 58(5-6), pp.681~697 (2010)[DOI]
  2. N. Castro Gonzalez, "New additive results for the g-Drazin inverse", Proc. Roy. Soc. Edinburgh Sect. A, 134(6), pp.1085~1097 (2004)[DOI]
  3. R. E. Cline, "A Drazin inverse for rectangular matrices", Linear Algebra Appl., 29, pp.53~62 (1980)[DOI]
  4. A. Dajic, "The weighted g-Drazin inverse for operators", J. Aust. Math. Soc., 82(2), pp.163~181 (2007)[DOI]
  5. M. P. Drazin, "Pseudo-inverses in associative rings and semigroups", Amer. Math. Monthly, 65, pp.506~514 (1958)[DOI]
  6. A. Hernandez, "Weighted binary relations involving the Drazin inverse", Appl. Math. Comput., 253, pp.215~223 (2015)
  7. A. Hernandez, "On some new pre-orders defined by weighted Drazin inverses", Appl. Math. Comput., 282, pp.108~116 (2016)
  8. J. J. Koliha, "A generalized Drazin inverse", Glasgow Math. J., 38(3), pp.367~381 (1996)[DOI]
  9. S. B. Malik, "On a new generalized inverse for matrices of an arbitrary index", Appl. Math. Comput., 226, pp.575~580 (2014)
  10. L. Meng, "The DMP inverse for rectangular matrices", Filomat, 31(19), pp.6015~6019 (2017)[DOI]
  11. D. Mosic, "The gDMP inverse of Hilbert space operators", Journal of Spectral Theory, 8(2), pp.555~573 (2018)[DOI]
  12. A. Yu, "Characterizations of DMP inverse in a Hilbert space", Calcolo, 53(3), pp.331~341 (2016)[DOI]

관련 논문AI추천

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