Schur complements in C*-algebras

Mathematische Nachrichten

Volumn 278, Issue 7-8, 2005, Pages 808-814

  Cvetković IIić, Dragana S ^a   Djordjević, Dragan S ^a   Rakočević, Vladimir ^a  

^a UNIVERSITY OF NI   (Serbia)

Author keywords

C* algebras; Generalized inverses; Idempotents; Schur complement

Indexed keywords

EID: 20444403429     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310273     Document Type: Article

References (23)

1. A. Albert, Conditions for positive and nonnegative definiteness in terms of pseudoinverses, SIAM J. Appl. Math. 17, No. 2, 434-440 (1969).
2. W. N. Anderson and R. J. Duffin, Series and parallel addition of matrices, J. Math. Anal. Appl. 26, 576-594 (1969).
3. W. N. Anderson and G. E. Trapp, Shorted operators II, SIAM J. Appl. Math. 28, 60-71 (1975).
4. T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26, 203-241 (1979).
5. T. Ando, Generalized Schur complements, Linear Algebra Appl. 27, 173-186 (1979).
6. D. Carlson, What are Schur complements, anyway?, Linear Algebra Appl. 74, 257-275 (1986).
7. D. Carlson, E. Haynsworth, and T. Markham, A generalization of the Schur complement by means of the Moore-Penrose inverse, SIAM J. Appl. Math. 26, 169-176 (1974).
8. D. J. Clements and H. K. Wimmer, Monotonicity of the optimal cost in the discrete-time regulator problem and Schur complements, Automatica 37, 1779-1786 (2001).
9. G. Corach, A. Maestripieri, and D. Stojanoff, Oblique projections and Schur complements, Acta Sci. Math. (Szeged) 67, 439-459 (2001).
10. W. Diffie and E. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory 22, No. 5, 644-654 (1976).
11. R. J. Duffin and G. E. Trapp, Hybrid addition of matrices - A network theory concept, Appl. Anal. 2, 241-254 (1972).
12. R. E. Harte, Invertibility and Singularity for Bounded Linear Operators (Marcel Dekker, New York, 1988).
13. R. E. Harte and M. Mbekhta, On generalized inverses in C*-algebras, Studia Math. 103, 71-77 (1992).
14. R. E. Harte and M. Mbekhta, On generalized inverses in C*-algebras, II, Studia Math. 106, 129-138 (1993).
15. E. Haynsworth, Determination of the inertia of a partitioned Hermitian matrix, Linear Algebra Appl. 1, 73-81 (1968).
16. J. J. Koliha, The Drazin and Moore-Penrose inverse in C*- algebras, Math. Proc. R. Ir. Acad. 99A, No. 1, 17-27 (1999).
17. J. J. Koliha, Range projections of idempotents in C*-algebras, Demonstratio Math. 34, No. 1, 91-103 (2001).
18. M. G. Krein, The theory of self-adjoint extensions of semi-bounded Hennitian operators and its applications, Math. Sb. (N. S.) 62, No. 20, 431-495 (1947).
19. C.-K. Li and R. Mathias, Extremal characterization of the Schur complements and resulting inequalities, SIAM Rev. 42, 233-246 (2000).
20. D. V. Quellette, Schur complements and statistics, Linear Algebra Appl. 36, 187-295 (1981).
21. V. Rakočević, Moore-Penrose inverse in Banach algebras, Proc. R. Ir. Acad. 88A, 57-60 (1988).
22. I. Schur, Über Potenzreihen die im Innern des Einheitskreises sind, J. Reine Angew. Math. 147, 205-234 (1917).
23. B.-Y. Wang, X. Zhang, and F. Zhang, Some inequalities on generalized Schur complements, Linear Algebra Appl. 302-303, 163-172 (1999).