Resolvent tests for similarity to a normal operator

Proceedings of the London Mathematical Society

Volumn 78, Issue 3, 1999, Pages 585-626

  Benamara, Nour Eddine ^a   Nikolski, Nikolai ^b  

^a MOULAY ISMAIL UNIVERSITY   (Morocco)

^b UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000913770     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611599001756     Document Type: Article

References (57)

1. L. DE BRANGES and J. ROVNYAK, 'Canonical models in quantum scattering theory', Perturbation theory and its application in quantum mechanics (Wiley, New York, 1966), pp. 295-391.
2. M. S. BRODSKII, Triangular and Jordan representations of linear operators (Nauka, Moscow, 1969);
3. Translations of Mathematical Monographs 32 (American Mathematical Society, Providence, R.I., 1971).
4. J. VAN CASTEREN, 'Operators similar to unitary or selfadjoint ones', Pacific J. Math. 104 (1983) 241-255.
5. K. CLANCEY, Seminormal operators, Lecture Notes in Mathematics 742 (Springer, Berlin, 1979).
6. D. N. CLARK, 'On a similarity theory for rational Toeplitz operators', J. Reine Angew. Math. 320 (1980) 6-31.
7. C. DAVIS and C. FOIAŞ, 'Operators with bounded characteristic functions and their J-unitary dilation', Acta Sci Math. (Szeged) 32 (1971) 127-139.
8. Y. DOMAR, 'On the existence of a large subharmonic minorant of a given function', Ark. Math. 3 (1957) 429-440.
9. N. DUNFORD and J. T. SCHWARTZ, Linear operators. III. Spectral operators (Wiley-Interscience, New York, 1971).
10. K. O. FRIEDRICHS, 'Über die Spektralzerlegung eines Integraloperators', Math. Ann. 115 (1938) 249-272.
11. K. O. FRIEDRICHS, 'On the perturbation of continuous spectra', Comm. Pure Appl. Math. 1 (1948) 361-406.
12. P. A. FUHRMANN, Linear systems and operators in Hilbert space (McGraw-Hill, New York, 1981).
13. T. W. GAMELIN, Uniform algebra (Prentice-Hall, Englewood Cliffs, New Jersey, 1969).
14. J. GARNETT, Bounded analytic functions (Academic Press, New York, 1981).
15. YU. P. GINSBURG, 'Multiplicative representations and minorants of analytic operator-functions', Funkcional. Anal. i Prilozen 1 (1967) no. 3, 9-23;
16. Funct. Anal. Appl. 1 (1967) no. 3, 180-192.
17. I. C. GOHBERG and M. G. KREIN, Introduction to the theory of linear nonselfadjoint operators (Nauka, Moscow, 1965);
18. Translations of Mathematical Monographs 18 (American Mathematical Society, Providence, R.I., 1969).
19. I. C. GOHBERG and M. G. KREIN, Theory of Volterra operators and its applications (Nauka, Moscow, 1967);
20. Translations of Mathematical Monographs 24 (American Mathematical Society, Providence, R.I., 1970).
21. I. C. GOHBERG and M. G. KREIN, 'On a description of contraction operators similar to unitary ones', Funkcional. Anal. i Prilozen 1 (1967) 38-60;
22. Funct. Anal. Appl. 1 (1967) 33-52.
23. n, Mathematical Reports 2, no. 1 (Harwood, London, 1984).
24. T. KATO, Perturbation theory for linear operators (Springer, New York, 1967).
25. A. S. MARKUS, 'Some tests for completeness of the system of root vectors of a linear operator in a Banach space', Mat. Sb. (N.S.) 70 (1966) 526-565;
26. Amer. Math. Soc. Transl. 85 (1969) no. 2.
27. P. MATTILA, Geometry of sets and measures in Euclidean spaces (Cambridge University Press, 1995).
28. S. N. NABOKO, 'Conditions for similarity to unitary and selfadjoint operators', Funkcional. Anal. i Prilozen 18 (1984) 16-27;
29. Funct. Anal. Appl. 18 (1984) 13-22.
30. N. NIKOLSKI, Treatise on the shift operator (Springer, Heidelberg, 1986).
31. N. NIKOLSKI, 'Yngve Domar's forty years in Harmonic Analysis', Acta Universitatis Upsaliensis 58 (1995) 45-78.
32. N. NIKOLSKI and S. V. KHRUSHCHEV, 'A function model and some problems in the spectral function theory', Trudy Math. Inst. Steklov 176 (1987) 97-210;
33. Proc. Steklov Inst. Math. 176 (1988) 111-214.
34. N. NIKOLSKI and V. I. VASYUNIN, 'Elements of spectral theory in terms of the free function model. Part I: Basic constructions', Holomorphic spaces (eds. Sh. Axler, J. McCarthy and D. Sarason), MSRI Publications 33 (MSRI, Berkeley, 1998), pp. 211-302.
35. V. V. PELLER, 'Spectrum, similarity, and invariant subspaces of Toeplitz operators', Izv. Akad. Nauk SSSR Ser. Math. 50 (1986) no. 4;
36. Math. USSR-Izv 29 (1987) 133-144.
37. C. POMMERENKE, Univalent functions (Vandenhoek and Ruprecht, Göttingen, 1975).
38. F. RIESZ and B. SZ.-NAGY, Leçons d'analyse fonctionnelle (Akadémiai Kiadò, Budapest, 1972).
39. L. A. SAHNOVICH, 'Reduction to diagonal form of non-selfadjoint operators with continuous spectrum', (Russian) Math. Sb. 44 (1958) 509-548.
40. L. A. SAHNOVICH, 'Non unitary operators with absolutely continuous spectrum', Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969) 52-64;
41. Math. USSR-Izv. 3 (1969) 51-63.
42. H. S. SHAPIRO, 'A class of singular functions', Canad. J. Math. 20 (1968) 1425-1431.
43. 1', Michigan Math. J. 11 (1964) 161-165.
44. B. SZ.-NAGY, 'On uniformly bounded linear transformations in Hilbert space', Acta Sci. Math. (Szeged) 11 (1947) 152-157.
45. B. SZ.-NAGY and C. FOIAŞ, Harmonic analysis of operators on Hilbert space (North-Holland, Amsterdam, and Akadémiai Kiadó, Budapest, 1970).
46. S. R. TREIL, 'Hankel operators, imbedding theorems, and bases of coinvariant subspaces of the multiple shift operator', Algebra i Analiz 1 (1989) no. 6, 200-234;
47. Leningrad Math. J. 1 (1990), no. 6, 1515-1548.
48. S. R. TREIL, 'Geometric methods in spectral theory of vector-valued functions: some recent results', Toeplitz operators and spectral function theory (ed. N. Nikolski), Operator Theory: Advances and Applications 42 (Birkhäuser, Basel, 1989), pp. 209-280.
49. V. I. VASYUNIN, 'Unconditionally convergent spectral decompositions and interpolation problems', Trudy Mat. Inst. Steklov 130 (1978) 5-49, 223;
50. Proc. Steklov Inst. Math. 4 (1979) 1-53.
51. V. I. VASYUNIN, 'The corona problem and the angles between invariant subspaces', Algebra i Analiz 6 (1994) 95-109;
52. St.-Petersburg Math. J. 6 (1995) 77-88.
53. J. WERMER, 'Commuting spectral operators on Hilbert space', Pacific J. Math. 4 (1954) 335-361.
54. D. R. YAFAEV, Mathematical scattering theory: general theory (University of St. Petersburg Publishers, 1994);
55. Translations of Mathematical Monographs 105 (American Mathematical Society, Providence, R.I., 1992).
56. D. V. YAKUBOVICH, 'Linearly similar models of the Toeplitz operator', Zap. Nauchn. sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 157 (1987) 113-123;
57. J. Soviet Math. 44 (1989) 826-833.