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On operator ranges


Author: Bhushan L. Wadhwa
Journal: Proc. Amer. Math. Soc. 80 (1980), 653-654
MSC: Primary 47A05; Secondary 47B20
DOI: https://doi.org/10.1090/S0002-9939-1980-0587947-8
MathSciNet review: 587947
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Abstract: If f is any vector-valued bounded function defined on open set D of the complex plane, and T is any bounded linear operator on a Hilbert space such that $ {\sigma _R}({T^ \ast })$ is empty and if $ {(T - zI)^2}f(z) = x$ for all z in D then f is analytic.


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

  • [1] K. Clancey, On local spectra of seminormal operators, Proc. Amer. Math. Soc. 72 (1978), 473-479. MR 509237 (80b:47031)
  • [2] R. G. Douglas, On majorization, factorization and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413-415. MR 0203464 (34:3315)
  • [3] N. Dunford and J. Schwartz, Linear operators. III: Spectral operators, Pure and Appl. Math., Vol. VII, Interscience, New York-London-Sydney, 1971. MR 0412888 (54:1009)
  • [4] B. E. Johnson, Continuity of linear operators commuting with continuous linear operators, Trans. Amer. Math. Soc. 128 (1967), 88-102. MR 0213894 (35:4748)
  • [5] C. R. Putnam, Ranges of normal and subnormal operators, Michigan Math. J. 18 (1971), 33-36. MR 0276810 (43:2550)
  • [6] -, Hyponormal contractions and strong power convergence, Pacific J. Math. 57 (1975), 531-538. MR 0380493 (52:1393)
  • [7] M. Radjabalipour, Ranges of hyponormal operators, Illinois J. Math. 21 (1977), 70-75. MR 0448140 (56:6449)
  • [8] J. G. Stampfli, Analytic extensions and spectral localization, J. Math. Mech. 19 (1966), 287-296. MR 0196500 (33:4687)
  • [9] J. G. Stampfli and B. L. Wadhwa, An asymmetric Putnam-Fuglede theorem for dominant operators, Indiana Univ. Math. J. 25 (1976), 359-365. MR 0410448 (53:14197)
  • [10] -, On dominant operators, Monatsh. Math. 84 (1977), 143-153. MR 0458225 (56:16428)

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DOI: https://doi.org/10.1090/S0002-9939-1980-0587947-8
Article copyright: © Copyright 1980 American Mathematical Society

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