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)



Continuity properties of the spectrum of operators on Lebesgue spaces

Author: Bruce A. Barnes
Journal: Proc. Amer. Math. Soc. 106 (1989), 415-421
MSC: Primary 47B38; Secondary 47A10
MathSciNet review: 969515
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Fix $ 1 \leq p \leq s \leq \infty $. Let $ {T_x},x \in \left[ {p,s} \right]$, be the collection of bounded linear operators on the Lebesgue spaces $ {L^x}$ determined by some fixed operator $ T$. This paper concerns continuity properties of the map $ x \to \sigma \left( {{T_x}} \right)$.

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

  • [1] B. Barnes, The spectrum of integral operators on Lebesgue spaces, J. of Operator Th. 18 (1987), 115-132. MR 912815 (89i:46065)
  • [2] -, Interpolation of spectrum of bounded operators on Lebesgue spaces, to appear in Rocky Mt. J. Math.
  • [3] -, Essential spectrum in a Banach algebra applied to linear operators, recently submitted.
  • [4] D. Boyd, The spectrum of the Cesàro operator, Acta. Sci. Math. 29 (1968), 31-34. MR 0239441 (39:798)
  • [5] K. Dayanithy, Interpolation of spectral operators, Math. Z. 159 (1978), 1-2. MR 488370 (80a:47048)
  • [6] N. Dunford and J. Schwartz, Linear operators, Part I, Interscience, New York-London, 1964.
  • [7] D. Herrero, Operator theory, Advances and Applications, Vol. 11, Birkhauser-Verlag, Basel, 1983, 191-232.
  • [8] J. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176. MR 0051441 (14:481b)
  • [9] J. Nieto, On the essential spectrum of symmetrizable operators, Math. Annalen 178 (1968), 145-153. MR 0233221 (38:1544)
  • [10] W. Rudin, Real and complex analysis, Third Ed., McGraw-Hill, New York, 1987. MR 924157 (88k:00002)
  • [11] E. Stout, The theory of uniform algebras, Bodgen & Quigley, Tanytown-on-Hudson, New York, 1971. MR 0423083 (54:11066)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B38, 47A10

Retrieve articles in all journals with MSC: 47B38, 47A10

Additional Information

Keywords: Linear operator, spectrum, spectral radius
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society