Abstract
Necessary and sufficient conditions are obtained for operator partial 2 × 2 matrices to have an idempotent completion, and all such completions are parametrically represented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T Ando, T Hara. Another approach to the strong Parrott theorem. J Math Anal Appl, 1992, 171(1): 125–130
M Bakonyi. Completion of operator partial matrices associated with chordal graphs. Integer Equat Oper Th, 1992, 15(1): 125–130
M Bakonyi, H J Woerdeman. On the strong Parrott completion problem. Proc Amer Math Soc, 1993, 117(2): 429–433
M-D Choi, J Hou, P Rosenthal. Completion of operator partial matrices to square-zero contractions. Lin Alg Appl 1997, 256: 1–30
C Davis. Completing a matrix so as to minimize the rank. Operator Theory: Adv Appl, Birkhauser, Basel, 1988, 29: 87–95
C Davis, W M Kahan, H F Weinberger. Norm-preserving dilations and their applications to optimal error estimates. SIAM J Numer Anal, 1982, 19(2): 445–469
H Du, C Gu. On the spectra of operator completion problems. Operator Theory: Adv Appl, Birkhauser, Basel, 1993, 64: 103–117
C Foias, A E Frazho. The Commutant Lifting Approach to Interpolation Problems. Operator Theory: Adv Appl, Birkhauser, Basel, 1990
C Foias, A Tannenbaunn. A strong Parrott theorem. Proc Amer Math Soc, 1989, 106(3): 777–784
P R Halmos. Subnormal suboperators and the subdiscrete topology. Anniversary Volume on Approximation Theory and Functional Analysis, Birkhauser Verlag Basel, 1984, 49–65
J Hou. Completions of operator partial matrices to projections. Lin Alg Appl, 1996, 246: 71–82
J Hou. On the spectra of positive completions for operator matrices. J Operator Theory, 1995, 33(2): 299–315
J Hou, H Du. Norm inequalities of positive operator matrices. Integ Equat Oper Th, 1995, 22(3): 281–294
C R Johnson, L Rodman. Completion of partial matrices to contractions. J Funct Anal, 1986, 69(2): 260–267
T Kidera, S Miyajima. Contractive completions of operator matrices. SUT J Math, 1991, 27(1): 49–71
S Parrott. On a quotient norm and the Sz, Nagy-Foias lifting theorem. J Funct Anal, 1978, 30(2): 311–328
V I Paulsen, L Rodman. Positive completions of matrices overC*-algebras. J Operator Theory, 1991, 25(2): 237–328
Z Sebestyen. Operator extensions on Hilbert space. Acta Sci Math (Szeged), 1993, 57(1): 233–248
D Timotin. A note on Parrott’s strong theorem. J Math Anal Appl, 1992, 171(1): 288–293
D Timotin. Completions of matrices and the commutant lifting theorem. J Funct Anal, 1992, 104(2): 291–298
H Radjavi, P Rosenthal. Invariant Subspaces. New York: Springer-Verlag, 1973
R G Douglas. On majorization, facterization and range inclusion of operators in Hilbert space. Proc Amer Math Soc, 1966, 17(3): 413–416
P A Fillmore, J P Williams. On operator ranges. Adv in Math, 1971, 7(6): 254–281
Author information
Authors and Affiliations
Additional information
Project supported by National Natural Science Foundation of China and Provincial Natural Science Foundation of Shanxi
Rights and permissions
About this article
Cite this article
Hou, J., Radjavi, H. & Rosenthal, P. Idempotent completions of operator partial matrices. Acta Mathematica Sinica 15, 333–346 (1999). https://doi.org/10.1007/BF02650728
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02650728