This is a preview of subscription content, log in via an institution to check access.
Literature Cited
Yu. P. Ginzburg, "J-nonexpanding operators in Hilbert space," Nauchn. Zapiski Odessk. Ped. In-ta,22, No. 1, 13–19 (1958).
Yu. P. Ginzburg, "Subspaces of a Hilbert space with an indefinite metric," Nauchn. Zapiski Odessk. Ped. In-ta,25, No. 2, 3–9 (1961).
R. S. Phillips, "Dissipative operators and hyperbolic systems of partial differential equations," Trans. Amer. Math. Soc.,90, No. 2, 193–254 (1959).
R. S. Phillips, "The extension of dual subspaces, invariant under an algebra," Proc. Internat. Sympos. on Linear Spaces, Jerusalem Acad. Press, Jerusalem (1960); Pergamon Press, Oxford—London—New York—Paris (1961), pp. 366–498.
Yu. P. Ginzburg and I. S. Iokhvidov, "Investigations in the geometry of infinite-dimensional spaces with a bilinear metric," Usp. Matem. Nauk,17, No. 4, 3–56 (1962).
M. G. Krein, "Introduction to the geometry of indefinite J-spaces and the theory of operators in these spaces," Vtoraya Letn. Matem. Shkola,I, Naukova Dumka, Kiev (1965), pp. 15–92.
M. G. Krein and Yu. L. Shmul'yan, "Plus-operators in a space with an indefinite metric," Matem. Issledovaniya (Kishinev),1, No. 1, 131–161 (1966).
Yu. L. Shmul'yan, "The theory of extensions of operators and spaces with an indefinite metric," Izv. Akad. Nauk SSSR, Ser. Matem.,38, 896–908 (1974).
E. Coddington, Extension Theory of Formally Normal and Symmetric Subspaces, Mem. Amer. Math. Soc., Vol. 134 (1973).
E. Coddington, "Self-adjoint subspace extensions of nondensely defined symmetric operators," Bull. Amer. Math. Soc.,79, No. 4, 712–715 (1973).
E. Coddington, "Self-adjoint subspace extensions of nondensely defined symmetric operators," Adv. Math.,14, No. 3, 309–332 (1974).
F. S. Rofe-Beketov, "Self-adjoint extensions of differential operators in a space of vector functions," Teoriya Funktsii, Funkts. Analiz i ikh Prilozheniya (Kharkov),8, 3–24 (1969).
S. MacLane, "An algebra of additive relations," Proc. Nat. Acad. Sci. USA,47, No. 7, 1043–1051 (1961).
R. Arens, "Operational calculus of linear relations," Pacific J. Math.,11, 9–23 (1961).
C. Bennevitz, "Symmetric relations on Hilbert spaces," Lect. Notes Math.,280, 212–218 (1972).
V. P. Glukhov, "Linear correspondences in spaces with an indefinite metric," Funktsional'. Analiz i Ego Prilozhen.,1, 37–46 (1973).
V. P. Glukhov, "Kelly transformations of linear correspondences," Funktsional'. Analiz i Ego Prilozhen.,1, 47–50 (1973).
V. P. Potapov, "The multiplicative structure of J-nonexpanding matrix functions," Trudy Mosk. Matem. O-va,4, 125–236 (1955).
Yu. P. Ginzburg, J-Nonexpanding Analytic Operator Functions [in Russian], Candidate's Dissertation, Odessa (1958).
I. M. Spitkovskii, "Recovery of a unitary operator from two of its diagonal blocks," Matem. Issledovaniya (Kishinev),8, No. 4, 187–193 (1973).
M. G. Krein and Yu. L. Shmul'yan, "Fractional-linear transformations with operator coefficients," Matem. Issledovaniya (Kishinev),2, No. 3, 64–96 (1967).
Additional information
Odessa Institute of Marine Engineers. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 10, No. 1, pp. 67–72, January–March, 1976.
Rights and permissions
About this article
Cite this article
Shmul'yan, Y.L. The theory of linear relations and spaces with an indefinite metric. Funct Anal Its Appl 10, 56–60 (1976). https://doi.org/10.1007/BF01075773
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01075773