Factorization of Operators in Krein Spaces and Linear-Fractional Relations of Operator Balls

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References

[1] S. L. Sobolev, “On the Motion of a Symmetric Top with a Cavity Filled with a Liquid,” Zh. Prikl. Mekhan. i Tekhn. Fiz., No. 3, 1960, pp. 20-55.

[2] L. S. Pontryagin, “Hermitian Operators in Spaces with Indefinite Metric,” Izvestiya Akademii Nauk SSSR, Seriya Matematicheskaya, Vol. 8, 1944, pp. 243-280.

[3] R. S. Phillips, “Dissipative Operators and Hyperbolic Systems of Partial Differential Equations,” Transactions of the American Mathematical Society, Vol. 90, No. 2, 1959, pp. 193-254.
doi:10.1090/S0002-9947-1959-0104919-1

[4] R. S. Phillips, “Dissipative Operators and Parabolic Partial Differential Equations,” Communications on Pure and Applied Mathematics, Vol. 12, No. 2, 1959, pp. 249-276. doi:10.1002/cpa.3160120206

[5] R. S. Phillips, “The Extensions of Dual Subspaces Invariant under an Algebra,” Proceedings of the International Symposium on Linear Spaces, Jerusalem, 5-12 July 1960, pp. 366-398.

[6] T. Ya. Azizov and I. S. Iokhvidov, “Foundations of Theory of Linear Operators in Spaces with Indefinite Metric,” Nauka, Moscow, 1986.

[7] M. G. Krein and Yu. L. Shmul’yan, “J-Polar Representation of Plus Operators,” Materialy Issledovaniya, Vol. 1, No. 2, 1966, pp. 172-210.

[8] V. A. Khatskevich, “Some Global Properties of Fractional-Linear Transformations,” Operator Theory, Vol. 73, 1994, pp. 355-361.

[9] V. A. Khatskevich and V. S. Shulman, “Operator Fractional-Linear Transformations: Convexity and Compactness of Image, Application,” Studia Mathematica, Vol. 116, No. 2, 1995, pp. 189-195.

[10] V. A. Khatskevich and L. Zelenko, “Indefinite Metrics and Dichotomy of Solutions for Linear Differential Equations in Hilbert Spaces,” Chinese Journal of Mathematics, Vol. 24, No. 2, 1996, pp. 99-112.

[11] V. A. Khatskevich and L. Zelenko, “The Fractional-Linear Transformations of the Operator Ball and Dichotomy of Solutions to Evaluation Equations,” Contemporary Mathematics, Vol. 204, 1997, pp. 149-154.
doi:10.1090/conm/204/02628

[12] V. A. Khatskevich, “Generalized Fractional Linear Transformations: Convexity and Compactness of the Image and the Pre-Image; Applications,” Studia Mathematica, Vol. 137, No. 2, 1999, pp. 169-175.

[13] V. A. Khatskevich and L. Zelenko, “Bistrict Plus-Operators in Krein Spaces and Dichotomous Behavior of Irreversible Dynamical Systems,” Operator Theory: Advances and Applications, Vol. 118, 2000, pp. 191-203.

[14] V. Khatskevich and V. A. Senderov, “On Convexity, Compactness, and Non-Emptiness of Images and Preimages of Operator Linear-Fractional Relations,” Doklady Akademii Nauk, Vol. 69, No. 3, 2004, pp. 409-411.

[15] T. Ya. Azizov, “On Extension of Invariant Dual Pairs,” Ukrainian Mathematical Journal, Vol. 41, No. 7, 1989, pp. 958-961. doi:10.1007/BF01060700

[16] V. Khatskevich, V. Senderov and V. Shulman, “On Operator Matrices Generating Linear Fractional Maps of Operator Balls,” Contemporary Mathematics, Vol. 364, 2004, pp. 93-102. doi:10.1090/conm/364/06679

[17] N. Dunford and J. Schwartz, “Linear Operators,” Wiley, New York, 1958.

[18] V. Khatskevich and V. A. Senderov, “On Operator Sets Generated by Plus-Operators,” Vestnik Voronezhskogo Gosudarstvennogo Universiteta, Seriya Fizika, Matematika, No. 2, 2010, pp. 170-174.

[19] V. Khatskevich, M. Ostrovskii and V. Shulman, “Linear Fractional Relations for Hilbert Space Operators,” Mathematische Nachrichten, Vol. 279, No. 8, 2006, pp. 875- 890. doi:10.1002/mana.200310400

[20] T. Azizov and V. Khatskevich, “A Theorem on Existence of Invariant Subspaces for J-Bi-Expansive Operators,” Operator Theory: Advances and Applications, Vol. 198, 2009, pp. 41-48.