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Almost normal operators, their spectra and invariant subspaces


Author: C. R. Putnam
Journal: Bull. Amer. Math. Soc. 79 (1973), 615-624
MSC (1970): Primary 47A10, 47A15, 47B15, 47B20; Secondary 47B05, 47B47
DOI: https://doi.org/10.1090/S0002-9904-1973-13241-0
MathSciNet review: 0338818
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  • 1. R. Arens, The maximal ideals of certain function algebras, Pacific J. Math. 8 (1958), 641-648. MR 22 #8315. MR 117537
  • 2. J. Bram, Subnormal operators, Duke Math. J. 22 (1955), 75-94. MR 16, 835. MR 68129
  • 3. A. Brown, On a class of operators, Proc. Amer. Math. Soc. 4 (1953), 723-728. MR 15, 538. MR 59483
  • 4. A. Brown and C. Pearcy, Spectra of tensor products of operators, Proc. Amer. Math. Soc. 17 (1966), 162-166. MR 32 #6218. MR 188786
  • 5. K. F. Clancey, Seminormal operators with compact self-commutators, Proc. Amer. Math. Soc. 26 (1970), 447-454. MR 42 #885. MR 265976
  • 6. K. F. Clancey, Examples of nonnormal seminormal operators whose spectra are not spectral sets, Proc. Amer. Math. Soc. 24 (1970), 797-800. MR 254643
  • 7. K. F. Clancey and C. R. Putnam, The local spectral behavior of completely subnormal operators, Trans. Amer. Math. Soc. 163 (1972), 239-244. MR 291844
  • 8. K. F. Clancey and C. R. Putnam, Normal parts of certain operators, J. Math. Soc. Japan 24 (1972), 198-203. MR 313843
  • 9. E. P. Dolženko, Approximation on closed regions and zero-sets, Dokl. Akad. Nauk SSR 143 (1962), 771-774—Soviet Math. Dokl. 3 (1962), 472-475. MR 24 #A2670.
  • 10. W. Donoghue, On a problem of Nieminen, Inst. Hautes Études Sci. Publ. Math. 16 (1963), 31-33. MR 27 #2864. MR 152892
  • 11. T. Furuta, On the class of paranormal operators, Proc. Japan Acad. 43 (1967), 594-598. MR 36 #4354. MR 221302
  • 12. T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood Cliffs, N. J., 1969. MR 410387
  • 13. K. Gustafson, State diagrams for Hilbert space operators, J. Math. Mech. 18 (1968/69), 33-45. MR 37 #3388. MR 227804
  • 14. P. R. Halmos, Normal dilations and extensions of operators, Summa Brasil. Math. 2 (1950), 125-134. MR 13, 359. MR 44036
  • 15. P. R. Halmos, Spectra and spectral manifolds, Ann. Soc. Polon. Math. 25 (1952), 43-49. MR 14, 1096. MR 55581
  • 16. P. R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N. J., 1967. MR 34 #8178. MR 208368
  • 17. P. Hartman, Aurel Wintner, J. London Math. Soc. 37 (1962), 483-503. MR 25 #4983. MR 141585
  • 18. F. Hartogs and A. Rosenthal, Über Folgen analytischer Funktionen, Math. Ann. 104 (1931), no. 1, 606–610 (German). MR 1512688, https://doi.org/10.1007/BF01457959
  • 19. V. Istratescu, T. Saitô and T. Yoshino, On a class of operators, Tôhoku Math. J. (2) 18 (1966), 410-413. MR 35 #756. MR 209860
  • 20. A. D. Joshi, Hyponormal polynomials of monotone shifts, Thesis, Purdue University, Fort Wayne, Ind., 1971.
  • 21. A. Lebow, On von Neumann's theory of spectral sets, J. Math. Anal. Appl. 7 (1963), 64-90. MR 27 #6149. MR 156220
  • 22. G. R. Luecke, Operators satisfying condition (G1) locally (to appear).
  • 23. J. von Neumann, Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes, Math. Nachr. 4 (1951), 258-281. MR 13, 254. MR 43386
  • 24. T. Nieminen, A condition for the self-adjointness of a linear operator, Ann. Acad. Sci. Fenn. Ser. A. I No. 316 (1962), 5 pp. MR 25 #2452. MR 139012
  • 25. C. R. Putnam, On the spectra of semi-normal operators, Trans. Amer. Math. Soc. 119(1965), 509-523. MR 32 #2913. MR 185446
  • 26. C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag, New York, 1967. MR 36, #707. MR 217618
  • 27. C. R. Putnam, The spectra of operators having resolvents of first-order growth, Trans. Amer. Math. Soc. 133 (1968), 505-510. MR 37 #4651. MR 229073
  • 28. C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 ( 1970), 323-330. MR 42 #5085. MR 270193
  • 29. C. R. Putnam, Ranges of normal and subnormal operators, Michigan Math J. 18 (1971), 33-36. MR 43 #2550. MR 276810
  • 30. C. R. Putnam, The spectra of completely hyponormal operators, Amer. J. Math. 93 (1971), 699-708. MR 43 #6757. MR 281038
  • 31. C. R. Putnam, Trace norm inequalities for the measure of hyponormal spectra, Indiana Univ. Math. J. 21 (1972), 775-779. MR 295131
  • 32. C. R. Putnam, A similarity between hyponormal and normal spectra, Illinois J. Math. 16 (1972), 695-702. MR 326462
  • 33. C. R. Putnam, The role of zero sets in the spectra of hyponormal operators (preprint). MR 333808
  • 34. C. R. Putnam, Resolvent vectors, invariant subspaces, and sets of zero capacity, Math. Ann. (to appear). MR 326428
  • 35. J. G. Stampfli, Hyponormal operators, Pacific J. Math. 12 (1962), 1453-1458. MR 26 #6772. MR 149282
  • 36. C. R. Putnam, Hyponormal operators and spectral density, Trans. Amer. Math. Soc. 117 (1965), 469-476. MR 30 #3375. MR 173161
  • 37. C. R. Putnam, Which weighted shifts are subnormal, Pacific J. Math. 17 (1966), 367-379. MR 33 #1740. MR 193520
  • 38. C. R. Putnam, A local spectral theory for operators, J. Functional Analysis 4 (1969), 1-10. MR 39 #4698. MR 243376
  • 39. C. R. Putnam, A local spectral theory for operators. II, Bull. Amer. Math. Soc. 75 (1969), 803-806. MR 39 #6108. MR 244794
  • 40. C. R. Putnam, A local spectral theory for operators. III : Resolvents, spectral sets and similarity, Trans. Amer. Math. Soc. 168 (1972), 133-151. MR 295114
  • 41. C. R. Putnam, A local spectral theory for operators. IV: Invariant subspaces, Indiana Univ. Math. J. 22(1972), 159-167. MR 296734
  • 42. B. Sz. -Nagy and C. Foiaş, Sur les contractions de l'espace de Hilbert. IX. Factorisations de la function caractéristique. Sous-espaces invariant, Acta Sci. Math. (Szeged) 25 (1964), 283-316. MR 31 #5101. MR 180871
  • 43. B. Wadhwa, A hyponormal operator whose spectrum is not a spectral set, Proc. Amer. Math. Soc. 38 (1973), 83-85. MR 310690
  • 44. J. Wermer, Report on subnormal operators, Report of an International Conference on Operator Theory and Group Representations, Arden House, Harriman, N. Y., 1955, pp. 1-3, Pub. #387, NAS-NRC, Washington, D. C., 1955. MR 17, 880. MR 76316
  • 45. Aurel Wintner, Zur Theorie der beschränkten Bilinearformen, Math. Z. 30 (1929), no. 1, 228–281 (German). MR 1545057, https://doi.org/10.1007/BF01187766
  • 46. L. Zalcman, Analytic capacity and rational approximation, Lecture Notes in Math., no. 50, Springer-Verlag, Berlin and New York, 1968. MR 37 #3018. MR 227434

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DOI: https://doi.org/10.1090/S0002-9904-1973-13241-0

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