Traces on irregular ideals
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- by József V. Varga PDF
- Proc. Amer. Math. Soc. 107 (1989), 715-723 Request permission
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
- C. K. Fong and H. Radjavi, On ideals and Lie ideals of compact operators, Math. Ann. 262 (1983), no. 1, 23–28. MR 690004, DOI 10.1007/BF01474167
- I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142
- B. S. Mitjagin, Normed ideals of intermediate type, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 819–832 (Russian). MR 0173935
- Norberto Salinas, Symmetric norm ideals and relative conjugate ideals, Trans. Amer. Math. Soc. 188 (1974), 213–240. MR 336371, DOI 10.1090/S0002-9947-1974-0336371-3
- József V. Varga, On unitary invariant ideals in the algebra of compact operators, Proc. Amer. Math. Soc. 108 (1990), no. 3, 789–794. MR 975661, DOI 10.1090/S0002-9939-1990-0975661-2
Additional Information
- © Copyright 1989 American Mathematical Society
- 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