Extremal
extensions of sectorial linear relations

Y. Arlinskii

1. Krein M.G. Theory of selfadjoint extensions of semibounded operators I,II // Mat. Sbornik. 1947. 20, ¹3. P.431–498; Mat. Sbornik. 1947. 21, ¹3. P.366–404.

2. Shtraus A.V. On extensions of semibounded operators // Dokl. Akad. Nauk SSSR. 1973. 211, ¹3. P.543–546.

3. Shtraus A.V. On the theory of extremal extensions of a bounded positive operator // Funktional. Anal. Ul'yanovsk. Gos. Ped. Inst. 1982, ¹18. P.115–126.

4. Ando T., Nishio K. Positive selfadjoint extensions of positive symmetric operators // Tohoku Math. Journ. 1970. 22. P.65–75.

5. Coddington E., de Snoo H.S.V. Positive selfadjoint extensions of positive symmetric subspaces // Mat. Z. 1978. 159. P.203–214.

6. Lyantse V.E., Storozh O.G. Methods of the theory of unbounded operators. – Kiev: Naukova Dumka, 1983.

7. Arlinskii Yu.M. Maximal sectorial extensions of sectorial operators // Dokl. Akad. Nauk Ukraine. 1993, ¹6. P.22–28.

8. Kato T. Perturbation theory of linear operators. – Moscow:Mir, 1972.

9. Kato T. Fractional powers of dissipative operators // Journ. Math. Soc. Japan. 1961. 13, ¹3. P.246–274.

10. Krein S.G. Linear differential equations in Banach space. – Moscow:Nauka, 1967.

11. Krein M.G., Ovcharenko I.E. On $Q$ -- functions and sc-resolvents of an Hermitian contraction with nondense domain // Sib. Mat. Zh. 1977. 18, ¹5. P.1032--1056.

12. Arlinskii Yu.M. On proper accretive extensions of positive linear relations // Ukr. Mat. Zh. 1995. 47, ¹6. P.723–730.

13. Derkach V.A., Malamud M.M. Weyl's function of Hermitian operator and its connection with characteristic function // Donetsk. 1985. Preprint, Akad. Nauk USSR. DonFTI.–85–9 (104).

14. Derkach V.A., Malamud M.M. Generalized resolvents and boundary value problems for Hermitian operators with gaps // Journ. Funct. Anal. 1991. 95, ¹1. P.1–95.

15. Derkach V.A., Malamud M.M., Tsekanovskii E.R. Sectorial extensions of positive operator and characteristic function // Ukr. Mat. Zh. 1989. 41, ¹2. P.151–158.

16. Storozh O.G. Extremal extensions of nonnegative operator and accretive boundary problems // Ukr. Mat. Zh. 1990. 42, ¹6. P.857–860.

17. Arlinskii Yu.M. On a class of extensions of $C(\alpha)$-suboperator // Dokl. Akad. Nauk Ukraine. 1992, ¹8. P.12--16.

18. Arlinskii Yu.M., Tsekanovskii E.R. Maximal sectorial extensions of positive Hermitian operators and their resolvents // Dokl. Akad. Nauk Armyan.SSR. 1984. 79, ¹5. P.12-16.

19. Kolmanovich V.Yu., Malamud M.M. Extensions of sectorial operators and dual pair of contractions // Donetsk. 1985. 57p. Deposited in VINITI, Moscow, ¹4428–85 DEP.

20. Gorbachuk V.I., Gorbachuk M.L., Kochubei A.N. Extension theory of symmetric operators and boundary value problems // Ukr. Mat. Zh. 1989. 41, ¹10. P.1298–1313.

21. Arlinskii Yu.M. Positive spaces of boundary values and sectorial extensions of nonnegative operator // Ukr. Mat. Zh. 1988. 40. ¹1. P.8–14.

	Extremal extensions of sectorial linear relations
Author	Y. Arlinskii East-Ukr. State Univ., Lugansk
Abstract	The Friedrichs and von Neumann extensions and a class of maximal sectorial extensions of a sectorial linear relation in a Hilbert space are studied.
Keywords	Friedrichs extension, von Neumann extension, maximal sectorial extensions, sectorial linear relation, Hilbert space
DOI	doi:10.30970/ms.7.1.81-96
Reference	1. Krein M.G. Theory of selfadjoint extensions of semibounded operators I,II // Mat. Sbornik. 1947. 20, ¹3. P.431–498; Mat. Sbornik. 1947. 21, ¹3. P.366–404. 2. Shtraus A.V. On extensions of semibounded operators // Dokl. Akad. Nauk SSSR. 1973. 211, ¹3. P.543–546. 3. Shtraus A.V. On the theory of extremal extensions of a bounded positive operator // Funktional. Anal. Ul'yanovsk. Gos. Ped. Inst. 1982, ¹18. P.115–126. 4. Ando T., Nishio K. Positive selfadjoint extensions of positive symmetric operators // Tohoku Math. Journ. 1970. 22. P.65–75. 5. Coddington E., de Snoo H.S.V. Positive selfadjoint extensions of positive symmetric subspaces // Mat. Z. 1978. 159. P.203–214. 6. Lyantse V.E., Storozh O.G. Methods of the theory of unbounded operators. – Kiev: Naukova Dumka, 1983. 7. Arlinskii Yu.M. Maximal sectorial extensions of sectorial operators // Dokl. Akad. Nauk Ukraine. 1993, ¹6. P.22–28. 8. Kato T. Perturbation theory of linear operators. – Moscow:Mir, 1972. 9. Kato T. Fractional powers of dissipative operators // Journ. Math. Soc. Japan. 1961. 13, ¹3. P.246–274. 10. Krein S.G. Linear differential equations in Banach space. – Moscow:Nauka, 1967. 11. Krein M.G., Ovcharenko I.E. On $Q$ -- functions and sc-resolvents of an Hermitian contraction with nondense domain // Sib. Mat. Zh. 1977. 18, ¹5. P.1032--1056. 12. Arlinskii Yu.M. On proper accretive extensions of positive linear relations // Ukr. Mat. Zh. 1995. 47, ¹6. P.723–730. 13. Derkach V.A., Malamud M.M. Weyl's function of Hermitian operator and its connection with characteristic function // Donetsk. 1985. Preprint, Akad. Nauk USSR. DonFTI.–85–9 (104). 14. Derkach V.A., Malamud M.M. Generalized resolvents and boundary value problems for Hermitian operators with gaps // Journ. Funct. Anal. 1991. 95, ¹1. P.1–95. 15. Derkach V.A., Malamud M.M., Tsekanovskii E.R. Sectorial extensions of positive operator and characteristic function // Ukr. Mat. Zh. 1989. 41, ¹2. P.151–158. 16. Storozh O.G. Extremal extensions of nonnegative operator and accretive boundary problems // Ukr. Mat. Zh. 1990. 42, ¹6. P.857–860. 17. Arlinskii Yu.M. On a class of extensions of $C(\alpha)$-suboperator // Dokl. Akad. Nauk Ukraine. 1992, ¹8. P.12--16. 18. Arlinskii Yu.M., Tsekanovskii E.R. Maximal sectorial extensions of positive Hermitian operators and their resolvents // Dokl. Akad. Nauk Armyan.SSR. 1984. 79, ¹5. P.12-16. 19. Kolmanovich V.Yu., Malamud M.M. Extensions of sectorial operators and dual pair of contractions // Donetsk. 1985. 57p. Deposited in VINITI, Moscow, ¹4428–85 DEP. 20. Gorbachuk V.I., Gorbachuk M.L., Kochubei A.N. Extension theory of symmetric operators and boundary value problems // Ukr. Mat. Zh. 1989. 41, ¹10. P.1298–1313. 21. Arlinskii Yu.M. Positive spaces of boundary values and sectorial extensions of nonnegative operator // Ukr. Mat. Zh. 1988. 40. ¹1. P.8–14.
Pages	81-96
Volume	7
Issue	1
Year	1997
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Extremal extensions of sectorial linear relations