A general factorization approach to the extension theory of nonnegative operators and relations

Journal of Operator Theory

Volumn 58, Issue 2, 2007, Pages 351-386

  Hassi, Seppo ^a   Sandovici, Adrian ^b   Snoo, Henk De ^c   Winkler, Henrik ^d  

^a UNIVERSITY OF VAASA   (Finland)

^b Colegiul Naţional Petru Rares ^*  (Romania)

^c UNIVERSITY OF GRONINGEN   (Netherlands)

^d TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Disjointness; Extremal extension.; Friedrichs extension; Kre n von Neumann extension; Nonnegative relation; Positive closability; Transversality

Indexed keywords

EID: 42149103880     PISSN: 03794024     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. T. ANDO, K. NISHIO, Positive selfadjoint extensions of positive symmetric operators, Tōhoku Math. J. 22(1970), 65-75.
2. R. ARENS, Operational calculus of linear relations, Pacific J. Math. 9(1961), 9-23.
3. Y.M. ARLINSKIǏ, Extremal extensions of sectorial linear relations, Math. Stud. 7(1997), 81-96.
4. Y.M. ARLINSKIǏ, S. HASSI, Z. SEBESTYÉN, H.S. V. dE SNOO, On the class of extremal extensions of a nonnegative operator, in Recent Advances in Operator Theory and Related Topics (Szeged, 1999), Oper. Theory Adv. Appl., vol. 127, Birkhauser, Basel 2001, pp. 41-81.
5. Y.M. ARLINSKIǏ, E.R. TSEKANOVSKIǏ, Quasi selfadjoint contractive extensions of Hermitian contractions, Teor. Funktsii Funktsional Anal, i Prilozhen 50(1988), 9-16.
6. Y.M. ARLINSKIǏ, E.R. TSEKANOVSKIǏ, The von Neumann problem for nonnegative symmetric operators, Integral Equations Operator Theory 51(2005), 319-356.
7. G. ARSENE, A. GHEONDEA, Completing matrix contractions, J. Operator Theory 7(1982), 179-189.
8. E.A. CODDINGTON, Extension theory of formally normal and symmetric subspaces, Mem. Amer. Math. Soc. 134(1973).
9. E.A. CODDINGTON, H.S.V. dE SNOO, Positive selfadjoint extensions of positive symmetric subspaces, Math. Z. 159(1978), 203-214.
10. V.A. DERKACH, S. HASSI, M.M. MALAMUD, H.S.V. DE SNOO, Boundary relations and their Weyl families, Trans. Amer. Math. Soc. 358(2006), 5351-5400.
11. V.A. DERKACH, M.M. MALAMUD, The extension theory of Hermitian operators and the moment problem, J. Math. Sci. 73(1995), 1-95.
12. P. FILLMORE, J. WILLIAMS, On operator ranges, Adv. Math. 7(1971), 254-281.
13. P.R. HALMOS, Subnormal suboperators and the discrete topology, in Anniversary Volume on Approximation Theory and Functional Analysis (Oberwolfach, 1983), Internat. Schriftenreihe Numer. Math., vol. 65, Birkhauser, Basel 1984, pp. 49-65.
14. S. HASSI, On the Friedrichs and the Kreǐn-von Neumann extension of nonnegative relations, in Contributions to Management Science, Mathematics and Modelling, Acta Wasaensia, vol. 122, Vaasan Yliopisto, Vaasa 2004, pp. 37-54.
15. 1 of Nevanlinna functions, J. Operator Theory 37(1997), 155-181.
16. S. HASSI, M.M. MALAMUD, H.S.V. dE SNOO, On Kreǐn's extension theory of non-negative operators, Math. Nachr. 274/275(2004), 40-73.
17. S. HASSI, A. SANDOVICI, H.S.V. dE SNOO, H. WINKLER, Form sums of nonnegative selfadjoint operators, Acta Math. Hungar. 111(2006), 81-105.
18. S. HASSI, A. SANDOVICI, H.S.V. dE SNOO, H. WINKLER, Extremal extensions for the sum of nonnegative selfadjoint relations, Proc. Amer. Math. Soc. 135(2007), 3193-3204.
19. S. HASSI, Z. SEBESTYEN, H.S.V. dE SNOO, On the nonnegativity of operator products, Acta Math. Hungar. 109(2005), 1-15.
20. S. HASSI, H.S.V. DE SNOO, One-dimensional graph perturbations of selfadjoint relations, Ann. Acad. Sci. Fenn. Ser. A I Math. 22(1997), 123-164.
21. S. HASSI, H.S.V. dE SNOO, F.H. SZAFRANIEC, Normal extensions of symmetric relations, in preparation.
22. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin 1980.
23. M.G. KREǏ;N, Theory of selfadjoint extensions of semibounded operators and its applications. I, II, Mat. Sb. 20, 21(1947), 431-495, 365-404.
24. M.M. MALAMUD, Some classes of extensions of a Hermitian operator with gaps [Russian], Ukrain. Mat. Zh. 44(1992), 215-233;
25. English Ukrainian Math. J. 44(1992), 190-204.
26. M.M. MALAMUD, On a formula of the generalized resolvents of a nondensely defined Hermitian operator [Russian], Ukrain. Mat. Zh. 44(1992), 1658-1688;
27. English Ukrainian Math. J. 44(1992), 1522-1547.
28. V. PROKAJ, Z. SEBESTYEN, On Friedrichs extensions of operators, Acta Sci. Math. (Szeged) 62(1996), 243-246.
29. V. PROKAJ, Z. SEBESTYÉN, On extremal positive operator extensions, Acta Sci. Math. (Szeged) 62(1996), 458-491.
30. Z. SEBESTYÉN, Restrictions of positive operators, Acta Sci. Math. (Szeged) 46(1983), 299-301.
31. Z. SEBESTYÉN, Operator extensions on Hilbert space, Acta Sci. Math. (Szeged) 57(1993), 233-248.
32. Z. SEBESTYÉN, E. SIKOLYA, On Kreǐn-von Neumann and Friedrichs extensions, Acta Sci. Math. (Szeged) 69(2003), 323-336.
33. Z. SEBESTYÉN, J. STOCHEL, Restrictions of positive self-adjoint operators, Acta Sci. Math. (Szeged) 55(1991), 149-154.
34. Z. SEBESTYÉN, J. STOCHEL, On products of unbounded operators, Acta Math. Hungar. 100(2003), 105-129.
35. Y.L. SHMUL'YAN, A Hellinger operator integral, Mat. Sb. 49(1959), 381-430.
36. Y.L. SHMUL'YAN, Two-sided division in a ring of operators, Math. Notes 1(1967), 400-403.
37. Y.L. SHMUL'YAN, R.N. YANOVSKAYA, On matrices whose entries are contractions, Izv. Vissh. Ucheb. Zaved. Matematica 7(1981), 72-75.
38. O.G. STOROZH, Extremal extensions of a nonnegative operator and accretive boundary problems, Ukrainian Math. J. 42(1990), 857-860.
39. A.V. ŠTRAUS, On extensions of semibounded operators, Dokl. Akad. Nauk SSSR 211(1973), 543-546.
40. A.V. ŠTRAUS, On the theory of extremal extensions of a bounded positive operator, Funkts. Anal. 18(1982), 115-126.