Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Symmetric norm ideals and relative conjugate ideals


Author: Norberto Salinas
Journal: Trans. Amer. Math. Soc. 188 (1974), 213-240
MSC: Primary 46L15
DOI: https://doi.org/10.1090/S0002-9947-1974-0336371-3
MathSciNet review: 0336371
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper some aspects of the algebraic structure of the ring of all bounded linear operators on an infinite dimensional separable complex Hilbert space are discussed. In particular, a comparison criterion for maximal and minimal norm ideals is established. Also, a general notion of the conjugate of an ideal relative to another ideal is studied and some questions concerning joins and intersections of ideals are solved.


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

  • [1] A. Brown, C. Pearcy and N. Salinas, Ideals of compact operators on Hilbert space, Michigan Math. J. 18 (1971), 373-384. MR 45 #909. MR 0291819 (45:909)
  • [2] 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 3, 208. MR 0005790 (3:208c)
  • [3] K. Fan, Maximum properties and inequalities for the eigenvalues of completely continuous operators, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 760-766. MR 13, 661. MR 0045952 (13:661e)
  • [4] D. J. H. Garling, On ideals of operators in Hilbert space, Proc. London Math. Soc. (3) 17 (1967), 115-138. MR 34 #8208. MR 0208398 (34:8208)
  • [5] I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators in Hilbert space, ``Nauka", Moscow, 1965; English transl., Transl. Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R. I., 1969. MR 36 #3137; 39 #7447. MR 0246142 (39:7447)
  • [6] I. C. Gohberg and M. G. Kreĭn, On the theory of triangular representations of non-selfadjoint operators, Dokl. Akad. Nauk SSSR 137 (1961), 1034-1037 = Soviet Math. Dokl. 2 (1961), 392-395. MR 25 #3370. MR 0139946 (25:3370)
  • [7] A. Horn, On the singular values of a product of completely continuous operators, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 374-375. MR 13, 565. MR 0045316 (13:565a)
  • [8] 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 30 #4142. MR 0173935 (30:4142)
  • [9] B. S. Mitjagin and A. S. Svarc, Functors in categories of Banach spaces, Uspehi Mat. Nauk 19 (1964), no. 2 (116), 65-130 = Russian Math. Surverys 19 (1964), no. 2, 65-127. MR 29 #3866. MR 0166593 (29:3866)
  • [10] N. Salinas, Ideal sets and ideals of compact operators on Hilbert space, Indiana Univ. Math. J. 22 (1972), 505-521. MR 0317094 (47:5642)
  • [11] -, Ideals of commutators of compact operators, Acta Sci. Math. (Szeged) (to appear). MR 0358425 (50:10891)
  • [12] R. Schatten, Norm ideals of completely continuous operators, Ergebnisse der Math. und ihrer Grenzgebiete, N. F., Heft 27, Springer-Verlag, Berlin, 1960. MR 22 #9878. MR 0119112 (22:9878)
  • [13] H. Weyl, Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 408-411. MR 11, 37. MR 0030693 (11:37d)
  • [14] A. Zaanen, Linear analysis. Measure and integral, Banach and Hilbert space, linear integral equations, Interscience, New York; North-Holland, Amsterdam; Noordhoff, Groningen, 1953. MR 15, 878. MR 0061752 (15:878b)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L15

Retrieve articles in all journals with MSC: 46L15


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0336371-3
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society