Skip to main content
    • Aa
    • Aa

2-convexity and 2-concavity in Schatten ideals

  • G. J. O. Jameson (a1)

The properties p-convexity and q-concavity are fundamental in the study of Banach sequence spaces (see [L-TzII]), and in recent years have been shown to be of great significance in the theory of the corresponding Schatten ideals ([G-TJ], [LP-P] and many other papers). In particular, the notions 2-convex and 2-concave are meaningful in Schatten ideals. It seems to have been noted only recently [LP-P] that a Schatten ideal has either of these properties if the underlying sequence space has. One way of establishing this is to use the fact that if (E, ‖ ‖E) is 2-convex, then there is another Banach sequence space (F, ‖ ‖F) such that ‖x;‖ = ‖x2F for all x ε E. The 2-concave case can then be deduced using duality, though this raises some difficulties, for example when E is inseparable.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[G-TJ]D. J. H. Garling and N. Tomczak-Jaegermann . The cotype and uniform convexity of unitary ideals. Israel J. Math. 45 (1983), 175197.

[L-Tz II]J. Lindenstrauss and L. Tzafriri . Classical Banach spaces II (Springer, 1979).

[LP-P]F. Lust-Piquard and G. Pisier . Non-commutative Khintchine and Paley inequalities. Arkiv för Matematik 29 (1991), 241260.

[R]S. Reisner . A factorization theorem in Banach lattices and its application to Lorentz spaces. Ann. Inst. Fourier 31 (1981), 239255.

[Sch]C. Schütt . Lorentz spaces that are isomorphic to subspaces of L1. Trans. Amer. Math. Soc. 314 (1989). 583595.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *