Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A hyponormal operator whose spectrum is not a spectral set


Author: Bhushan L. Wadhwa
Journal: Proc. Amer. Math. Soc. 38 (1973), 83-85
DOI: https://doi.org/10.1090/S0002-9939-1973-0310690-3
MathSciNet review: 0310690
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: Clancey has given an example of a hyponormal, nonnormal operator whose spectrum is thin and hence not a spectral set. In this note, using fairly simple techniques, we give an example of a hyponormal operator whose spectrum contains a disc and is not a spectral set.


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

  • [1] S. K. Berberian, A note on operators whose spectrum is a spectral set, Acta. Sci. Math. (Szeged) 27 (1966), 201-203. MR 34 #3309. MR 0203458 (34:3309)
  • [2] K. F. Clancey, Examples of nonnormal seminormal operators whose spectra are not spectral sets, Proc. Amer. Math. Soc. 24 (1970), 797-800. MR 40 #7851. MR 0254643 (40:7851)
  • [3] I. Colojoara and C. Foias, Theory of generalized spectral operators, Gordon and Breach, New York, 1968. MR 0394282 (52:15085)
  • [4] A. Lebow, On von Neumann's theory of spectral sets, J. Math. Anal. Appl. 7 (1963), 64-90. MR 27 #6149. MR 0156220 (27:6149)
  • [5] F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Akad. Kiadó, Budapest, 1953; English transl., Ungar, New York, 1955. MR 15, 132; MR 17, 175. MR 0056821 (15:132d)
  • [6] J. P. Williams, Minimal spectral sets of compact operators, Acta. Sci. Math. (Szeged) 28 (1967), 93-106. MR 36 #725. MR 0217636 (36:725)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310690-3
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society