Search Results - Clasificación AMS::47 Operator theory::47A General theory of linear operators

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    Authors: Civin, Paul

    Source: The American Mathematical Monthly, 1960 Feb 01. 67(2), 199-199.

    Relation: Linear Operators. Part I: General Theory. N. Dunford J. T. Schwartz

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    Subject Terms: msc:47E05

    File Description: application/pdf

    Relation: mr:MR654055; zbl:Zbl 0505.45003; reference:[1] R. C. Brown, A. M. Krall: $n$-th order ordinary differential systems under Stieltjes boundary conditions.Czech. Math. J. 27 (102) (1977), 119-131. Zbl 0369.34006, MR 0430394; reference:[2] R. C. Brown, M. Tvrdý: Generalized boundary value problems with abstract side conditions and their adjoints I.Czech. Math. J., 30 (105) (1980), 7-27. MR 0565904; reference:[3] R. N. Bryan: A nonhomogeneous linear differential system with interface conditions.Proc. AMS 22 (1969), 270-276. Zbl 0201.11002, MR 0241739; reference:[4] E. A. Coddington, A. Dijksma: Adjoint subspaces in Banach spaces with applications to ordinary differential subspaces.Annali di Mat. Рurа ed Appl., CXVIII (1978), 1 - 118. Zbl 0408.47035, MR 0533601; reference:[5] R. Conti: On ordinary differential equations with interface conditions.J. Diff. Eq. 4 (1968), 4-11. Zbl 0157.14104, MR 0218642, 10.1016/0022-0396(68)90045-4; reference:[6] A. Gonelli: Un teorema di esistenza per un problema di tipo interface.Le Matematiche, 22 (1967), 203-211. MR 0240380; reference:[7] K. Jörgens: Lineare Integraloperatoren.В. G. Teubner Stuttgart, 1970. MR 0461049; reference:[8] J. L. Kelley, I. Namioka: Linear Topological Spaces.Van Nostrand, Princeton, New Jersey, 1963. Zbl 0115.09902, MR 0166578; reference:[9] A. M. Krall: Differential operators and their adjoints under integral and multiple point boundary conditions.J. Diff. Eq. 4 (1968), 327-336. Zbl 0165.42702, MR 0230968, 10.1016/0022-0396(68)90019-3; reference:[10] V. P. Maksimov: The property of being Noetherian of the general boundary value problem for a linear functional differential equation.(in Russian), Diff. Urav. 10 (1974), 2288-2291. MR 0361355; reference:[11] V. P. Maksimov, L. F. Rahmatullina: A linear functional-differential equation that is solved with respect to the derivative.(in Russian) Diff. Urav. 9 (1973), 2231-2240. MR 0333397; reference:[12] I. P. Natanson: Theory of Functions of a Real Variable.Frederick Ungar, New York. MR 0067952; reference:[13] J. V. Parhimovič: Multipoint boundary value problems for linear integro-differential equations in the class of smooth functions.(in Russian), Diff. Urav. 8 (1972), 549-552. MR 0298370; reference:[14] J. V. Parhimovič: The index and normal solvability of a multipoint boundary value problem for an integro-differential equation.(in Russian), Vesci Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, 1972, 91-93. MR 0305154; reference:[15] Št. Schwabik: Differential equations with interface condtions.Časopis pěst. mat. 105 (1980), 391-408. MR 0597916; reference:[16] Št. Schwabik M. Tvrdý, O. Vejvoda: Differential and Integral Equations: Boundary Value Problems and Ajoints.Academia, Praha, 1979. MR 0542283; reference:[17] F. W. Stallard: Differential systems with interface conditions.Oak Ridge Nat. Lab. Publ. No. 1876 (Physics).; reference:[18] M. Tvrdý: Linear functional-differential operators: normal solvability and adjoints.Colloquia Mathematica Soc. János Bolyai, 15, Differential Equations, Keszthely (Hungary), 1975, 379-389. MR 0482357; reference:[19] M. Tvrdý: Linear boundary value type problems for functional-differential equations and their adjoints.Czech. Math. J. 25 (100), (1975), 37-66. MR 0374609; reference:[20] M. Tvrdý: Boundary value problems for generalized linear differential equations and their adjoints.Czech. Math. J. 23 (98) (1973), 183-217. MR 0320417; reference:[21] A Zettl: Adjoint and self-adjoint boundary value problems with interface conditions.SIAM J. Appl. Math. 16 (1968), 851-859. Zbl 0162.11201, MR 0234049, 10.1137/0116069

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    Authors: Gil', Michael

    File Description: application/pdf

    Relation: mr:MR4764540; zbl:Zbl 07893399; reference:[1] Abdelmoumen, B., Jeribi, A., Mnif, M.: Invariance of the Schechter essential spectrum under polynomially compact operator perturbation.Extr. Math. 26 (2011), 61-73. Zbl 1283.47007, MR 2908391; reference:[2] Aiena, P., Triolo, S.: Some perturbation results through localized SVEP.Acta Sci. Math. 82 (2016), 205-219. Zbl 1374.47006, MR 3526346, 10.14232/actasm-014-785-1; reference:[3] Bhatia, R., Davis, C.: Perturbation of extended enumerations of eigenvalues.Acta Sci. Math. 65 (1999), 277-286. Zbl 0933.47015, MR 1702207; reference:[4] Bhatia, R., Elsner, L.: The Hoffman-Wielandt inequality in infinite dimensions.Proc. Indian Acad. Sci., Math. Sci. 104 (1994), 483-494. Zbl 0805.47017, MR 1314392, 10.1007/BF02867116; reference:[5] Chaker, W., Jeribi, A., Krichen, B.: Demicompact linear operators, essential spectrum and some perturbation results.Math. Nachr. 288 (2015), 1476-1486. Zbl 1343.47015, MR 3395822, 10.1002/mana.201200007; reference:[6] Gil', M. I.: Lower bounds for eigenvalues of Schatten-von Neumann operators.JIPAM, J. Inequal. Pure Appl. Math. 8 (2007), Article ID 66, 7 pages. Zbl 1133.47016, MR 2345921; reference:[7] Gil', M. I.: Sums of real parts of eigenvalues of perturbed matrices.J. Math. Inequal. 4 (2010), 517-522. Zbl 1213.15016, MR 2777268, 10.7153/jmi-04-46; reference:[8] Gil', M. I.: Bounds for eigenvalues of Schatten-von Neumann operators via self-commutators.J. Funct. Anal. 267 (2014), 3500-3506. Zbl 1359.47016, MR 3261118, 10.1016/j.jfa.2014.06.019; reference:[9] Gil', M. I.: A bound for imaginary parts of eigenvalues of Hilbert-Schmidt operators.Funct. Anal. Approx. Comput. 7 (2015), 35-38. Zbl 1355.47011, MR 3313254; reference:[10] Gil', M. I.: Inequalities for eigenvalues of compact operators in a Hilbert space.Commun. Contemp. Math. 18 (2016), Article ID 1550022, 5 pages. Zbl 1336.47022, MR 3454622, 10.1142/S0219199715500224; reference:[11] Gil', M. I.: Operator Functions and Operator Equations.World Scientific, Hackensack (2018). Zbl 1422.47004, MR 3751395, 10.1142/10482; reference:[12] Gil', M. I.: Norm estimates for resolvents of linear operators in a Banach space and spectral variations.Adv. Oper. Theory 4 (2019), 113-139. Zbl 06946446, MR 3867337, 10.15352/aot.1801-1293; reference:[13] Gil', M. I.: On matching distance between eigenvalues of unbounded operators.Constr. Math. Anal. 5 (2022), 46-53. Zbl 1497.47009, MR 4410203, 10.33205/cma.1060718; reference:[14] Gohberg, I. C., Krein, M. G.: Introduction to the Theory of Linear Nonselfadjoint Operators.Translations of Mathematical Monographs 18. AMS, Providence (1969). Zbl 0181.13503, MR 0246142, 10.1090/mmono/018; reference:[15] Gohberg, I. C., Krein, M. G.: Theory and Applications of Volterra Operators in a Hilbert Space.Translations of Mathematical Monographs 24. AMS, Providence (1970). Zbl 0194.43804, MR 0264447, 10.1090/mmono/024; reference:[16] Jeribi, A.: Perturbation Theory for Linear Operators: Denseness and Bases with Applications.Springer, Singapore (2021). Zbl 1483.47001, MR 4306622, 10.1007/978-981-16-2528-2; reference:[17] Kahan, W.: Spectra of nearly Hermitian matrices.Proc. Am. Math. Soc. 48 (1975), 11-17. Zbl 0322.15022, MR 0369394, 10.1090/S0002-9939-1975-0369394-5; reference:[18] Kato, T.: Perturbation Theory for Linear Operators.Grundlehren der mathematischen Wissenschaften 132. Springer, Berlin (1980). Zbl 0435.47001, MR 0407617, 10.1007/978-3-642-66282-9; reference:[19] Kato, T.: Variation of discrete spectra.Commun. Math. Phys. 111 (1987), 501-504. Zbl 0632.47002, MR 0900507, 10.1007/BF01238911; reference:[20] Killip, R.: Perturbations of one-dimensional Schrödinger operators preserving the absolutely continuous spectrum.Int. Math. Res. Not. 2002 (2002), 2029-2061. Zbl 1021.34071, MR 1925875, 10.1155/S1073792802204250; reference:[21] Ma, R., Wang, H., Elsanosi, M.: Spectrum of a linear fourth-order differential operator and its applications.Math. Nachr. 286 (2013), 1805-1819. Zbl 1298.34041, MR 3145173, 10.1002/mana.201200288; reference:[22] Rojo, O.: Inequalities involving the mean and the standard deviation of nonnegative real numbers.J. Inequal. Appl. 2006 (2006), Article ID 43465, 15 pages. Zbl 1133.26321, MR 2270311, 10.1155/JIA/2006/43465; reference:[23] Sahari, M. L., Taha, A. K., Randriamihamison, L.: A note on the spectrum of diagonal perturbation of weighted shift operator.Matematiche 74 (2019), 35-47. Zbl 1714.2751, MR 3964778, 10.4418/2019.74.1.3

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    Source: Proceedings: Mathematical, Physical and Engineering Sciences, 2013 Jun 01. 469(2154), 1-21.