A series representation for the generalized inverse of a closed linear operator

Lawrence J. Lardy

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1975)

  • Volume: 58, Issue: 2, page 152-157
  • ISSN: 0392-7881

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Lardy, Lawrence J.. "A series representation for the generalized inverse of a closed linear operator." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 58.2 (1975): 152-157. <http://eudml.org/doc/291206>.

@article{Lardy1975,
author = {Lardy, Lawrence J.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {2},
number = {2},
pages = {152-157},
publisher = {Accademia Nazionale dei Lincei},
title = {A series representation for the generalized inverse of a closed linear operator},
url = {http://eudml.org/doc/291206},
volume = {58},
year = {1975},
}

TY - JOUR
AU - Lardy, Lawrence J.
TI - A series representation for the generalized inverse of a closed linear operator
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1975/2//
PB - Accademia Nazionale dei Lincei
VL - 58
IS - 2
SP - 152
EP - 157
LA - eng
UR - http://eudml.org/doc/291206
ER -

References

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  1. ARGHIRIADE, E. (1968) - Sur l'inverse généralisée d'un opérateur linéaire dans les espaces de Hilbert, «Atti Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.», Ser. VIII, 45, 471-477. Zbl0186.45103MR247440
  2. ARGHIRIADE, E. and DRAGOMIR, A. (1969) - Remarques sur quelques théorems relatives l'inverse généralisée d'un opérateur linéaire dans les espaces de Hilbert, «Atti Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.», Ser. VIII, 46, 333-338. Zbl0186.45104MR256140
  3. BEN-ISRAEL, A. and CHARNES, A. (1963) - Contributions to the theory of generalized inverses, «SIAM J. Appl. Math.», 11, 667-699. Zbl0116.32202MR179192
  4. GOLDBERG, S. (1966) - Unbounded Linear Operators, McGraw-Hill, New York. Zbl0148.12501MR200692
  5. HESTENES, M. R. (1961) - Relative self-adjoint operators in Hilbert spaces, «Pacific J. Math.», 11, 1315-1357. Zbl0171.34601MR136996
  6. KÄMMERER, W. J. and NASHED, M. Z. (1971) - Steepest descent for singular linear operators with nonclosed range, «Applicable Analysis», 1, 143-159. Zbl0212.15802MR290134DOI10.1080/00036817108839011
  7. NASHED, M. Z. (1971) - Generalized inverses, normal solvability, and iteration for singular operator equations, in Nonlinear Functional Analysis and Applications, Edited by Louis B. Rail, Academic Press, New York. Zbl0236.41015MR275246
  8. PETRYSHYN, W. V. (1967) - On generalized inverses and uniform convergence of ( I - β ⁢ K ) n with applications to iterative methods, «J. Math. Anal. Appl.», 18, 417-439. Zbl0189.47502MR208381DOI10.1016/0022-247X(67)90036-4
  9. REISZ, F. and NAGY, B. SZ. (1955) - Functional Analysis, Frederick Ungar, New York. MR71727
  10. SHOWALTER, D. (1967) - Representation and computation of the pseudoinverse, «Proc. Amer. Soc.», 18, 584-586. Zbl0148.38205MR212594DOI10.2307/2035419
  11. SHOWALTER, D. and BEN-ISRAEL, A. (1970) - Representation and computation of the generalized inverse of a bounded linear operator between Hilbert spaces, «Atti Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.», 48, 184-193. Zbl0202.41703MR273432
  12. TSENG, YU. YA. (1949) - Sur les solutions des equations opératrices fonctionnelles entre les espaces unitaires. Solutions extremales. Solutions virtuelles, «C.R. Acad. Sci. Paris», 228, 640-641. Zbl0034.37302MR29479
  13. TSENG, YU. YA. (1949) - Generalized inverses of unbounded operators between two unitary spaces, «Dokl. Akad. Nauk SSSR (N.S.)», 67, 431-434. MR31191
  14. TSENG, YU. YA. (1949) - Properties and classification of generalized inverses of closed operators, «Dokl. Akad. Nauk. SSSR (N.S.)», 67, 607-610. MR31192
  15. TSENG, YU. YA. (1956) - Virtual solutions and generalized inverse, «Uspehi Math. Nauk. (N.S.)», 11, 213-215. MR83710
  16. WYLER, O. (1964) - Green's operators, «Ann. Mat. Pura Appl.», 66, 251-264. Zbl0197.39301MR173963DOI10.1007/BF02412445

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