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)

 
 

 

Generalized scalar operators as dilations


Authors: Hari Bercovici and Srdjan Petrović
Journal: Proc. Amer. Math. Soc. 123 (1995), 2173-2180
MSC: Primary 47A20; Secondary 47A45, 47B40
DOI: https://doi.org/10.1090/S0002-9939-1995-1246516-8
MathSciNet review: 1246516
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that polynomially bounded operators on Banach spaces have polynomially bounded dilations which have spectrum in the unit circle and are generalized scalar. The proof also yields a description of all compressions of generalized scalar operators with spectrum in the unit circle.


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

  • [1] I. Colojoară and C. Foias, Theory of generalized spectral operators, Gordon and Breach, New York, 1968. MR 0394282 (52:15085)
  • [2] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. MR 0270173 (42:5066)
  • [3] S. Petrović, A dilation theory for polynomially bounded operators, J. Funct. Anal. 108 (1992), 458-469. MR 1176683 (93j:47008)
  • [4] -, On the resolvent of a dilation for polynomially bounded operators, Integral Equations Operator Theory 20 (1994), 364-376. MR 1299894 (95k:47012)
  • [5] B. Sz.-Nagy, Sur les contractions de l'espace de Hilbert, Acta Sci. Math. (Szeged) 15 (1953), 87-92. MR 0058128 (15:326d)
  • [6] B. Sz.-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970. MR 0275190 (43:947)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A20, 47A45, 47B40

Retrieve articles in all journals with MSC: 47A20, 47A45, 47B40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1246516-8
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society