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)

 
 

 

Traces on irregular ideals


Author: József V. Varga
Journal: Proc. Amer. Math. Soc. 107 (1989), 715-723
MSC: Primary 47D25; Secondary 47B07, 47B10, 47D30
DOI: https://doi.org/10.1090/S0002-9939-1989-0984818-8
MathSciNet review: 984818
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Simple answers are given to the following and related questions: For what Hilbert space operator $ A$ is it true that the smallest ideal (alternatively, the smallest norm ideal, the smallest maximal norm ideal) containing $ A$ is a norm (an intermediate norm, a principal norm) ideal? Do these ideals support a nontrivial unitary invariant positive linear functional?


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

  • [1] C. K. Fong and H. Radjavi, On ideals and Lie ideals of compact operators, Math. Ann. B 262 (1963), 23-28. MR 690004 (84d:47059)
  • [2] I. C. Gohberg and M. G. Krein, Introduction to the theory of nonselfadjoint operators, Trans. Amer. Math. Soc., Vol. 18, Providence, R.I., 1969. MR 0246142 (39:7447)
  • [3] B. S. Mitjagin, Normed ideals of intermediate type, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 819-832; English transl., Amer. Math. Soc. Transl. (2) 63 (1967), 180-194. MR 0173935 (30:4142)
  • [4] N. Salinas, Symmetric norm ideals and relative conjugate ideals, Trans. Amer. Math. Soc. 188 (1974), 213-240. MR 0336371 (49:1146)
  • [5] J. V. Varga, On unitary invariant ideals in the algebra of compact operators (to appear). MR 975661 (90m:47060)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D25, 47B07, 47B10, 47D30

Retrieve articles in all journals with MSC: 47D25, 47B07, 47B10, 47D30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0984818-8
Keywords: Compact operator, principal ideal, unitary invariance, $ s$-numbers
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society