Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Curvatures and similarity of operators with holomorphic eigenvectors


Author: Mitsuru Uchiyama
Journal: Trans. Amer. Math. Soc. 319 (1990), 405-415
MSC: Primary 47A45
DOI: https://doi.org/10.1090/S0002-9947-1990-0968421-4
MathSciNet review: 968421
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The curvature of the holomorphic vector bundle generated by eigenvectors of operators is estimated, and the necessary and sufficient conditions for contractions to be similar or quasi-similar with unilateral shifts are given.


References [Enhancements On Off] (What's this?)

  • [1] V. T. Alexander, Construction operators quasisimilar to a unilateral shift, Trans. Amer. Math. Soc. 283 (1984), 697-703. MR 737893 (85e:47009)
  • [2] S. Bergman, The kernel function and conformal mapping, 2nd ed., Math. Surveys, no. 5, Amer. Math. Soc., Providence, R. I., 1970. MR 0507701 (58:22502)
  • [3] J. A. Van Casteren, A problem of Sz.-Nagy, Acta Sci. Math. 42 (1980), 189-194. MR 576954 (81g:47017)
  • [4] M. J. Cowen and R. G. Douglas, Complex geometry and operator theory, Acta Math. 141 (1978), 187-261. MR 501368 (80f:47012)
  • [5] -, Operators possessing an open set of eigenvalues, Colloq. Math. Soc. János Bolyai 35, North-Holland, Amsterdam, 1980, pp. 323-341. MR 751007 (85k:47033)
  • [6] P. A. Fuhrmann, On the corona theorem and its application to spectral problems in Hilbert space, Trans. Amer. Math. Soc. 132 (1968), 55-66. MR 0222701 (36:5751)
  • [7] G. M. Goluzin, Geometric theory of functions of a complex variable, Transl. Math. Monographs, Amer. Math. Soc., Providence, R. I., 1969. MR 0247039 (40:308)
  • [8] H. Helson, Lectures on invariant subspaces, Academic Press, 1964. MR 0171178 (30:1409)
  • [9] G. Misra, Curvature inequality and extremal properties of bundle shifts, J. Operator Theory 11 (1984), 305-317. MR 749164 (86h:47057)
  • [10] -, Curvature and the backward shift operators, Proc. Amer. Math. Soc. 91 (1984), 105-107. MR 735574 (86b:47048)
  • [11] M. Rosenblum, A corona theorem for countably many functions, Integral Equations and Operator Theory 3 (1980), 125-137. MR 570865 (81e:46034)
  • [12] K. Seddighi, Essential spectra of operators in $ {B_n}(\Omega )$, Proc. Amer. Math. Soc. 87 (1983), 453-458. MR 684638 (84e:47022)
  • [13] A. Shields, Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys, no. 13, Amer. Math. Soc., Providence, R. I., 1974, pp. 49-128. MR 0361899 (50:14341)
  • [14] B. Sz.-Nagy and C. Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland, 1970. MR 0275190 (43:947)
  • [15] B. Sz.-Nagy and C. Foias, On contractions similar to isometries and Toeplitz operators, Ann. Acad. Sci. Fenn. 2 (1976), 553-564. MR 0634808 (58:30376)
  • [16] K. Takahashi, On quasiaffine transform of unilateral shifts, Proc. Amer. Math. Soc. 100 (1987), 683-687. MR 894438 (88h:47025)
  • [17] M. Uchiyama, Contractions and unilateral shifts, Acta Sci. Math. 46 (1983), 345-356. MR 739054 (85e:47011)
  • [18] -, Contractions with $ (\sigma,c)$ defect operators, J. Operator Theory 12 (1984), 221-233. MR 757432 (85j:47017)
  • [19] R. O. Wells, Differential analysis on complex manifolds, Prentice-Hall, Englewood Cliffs, N. J., 1973. MR 0515872 (58:24309a)
  • [20] P. Y. Wu, Contractions quasisimilar to an isometry, preprint. MR 1018682 (90m:47029)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47A45

Retrieve articles in all journals with MSC: 47A45


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0968421-4
Keywords: Curvature of holomorphic vector bundle, Szegà kernel, contraction, quasi-similar, similar, Hardy class, corona theorem, eigenvector, canonical model theory
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society