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)



Essentially Hermitian operators on $ l\sb{1}$ are compact perturbations of Hermitians

Authors: David Legg and Joseph Ward
Journal: Proc. Amer. Math. Soc. 67 (1977), 224-226
MSC: Primary 47A55; Secondary 47B99
MathSciNet review: 0458210
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we present a solution to one case of a problem of F. F. Bonsall; namely, that every essentially Hermitian operator on $ {l_1}$ is a compact perturbation of a Hermitian operator.

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

  • [1] F. F. Bonsall, Hermitian operators on Banach spaces, Hilbert Space and Operator Algebras, Colloq. Math. Soc. Janos Bolyai, 5, North-Holland, Amsterdam 1972, 65-75. MR 0358413 (50:10879)
  • [2] F. F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and of elements of normed algebras, Cambridge Univ. Press, Cambridge, 1971. MR 0288583 (44:5779)
  • [3] -, Numerical ranges II, Cambridge Univ. Press, Cambridge, 1973. MR 0442682 (56:1063)
  • [4] J. W. Calkin, Two-sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. (2) 42 (1941), 839-873. MR 0005790 (3:208c)
  • [5] C. K. Chui, P. W. Smith, R. R. Smith and J. D. Ward, L-ideals and numerical range preservation, Illinois J. Math. 21 (1977), 365-373. MR 0430817 (55:3822)
  • [6] J. G. Stampfli, Compact perturbations, normal eigenvalues, and a problem of Salinas, J. London Math. Soc. 2 (1974), 165-175. MR 0365196 (51:1449)
  • [7] A. E. Taylor, Introduction to functional analysis, Wiley, New York, 1958. MR 0098966 (20:5411)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A55, 47B99

Retrieve articles in all journals with MSC: 47A55, 47B99

Additional Information

Keywords: Numerical range, Hermitian operator on a Banach space, generalized Banach limit
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society