Publication: Duality and Lorentz-Marcinkiewicz Operator-Spaces
Loading...
Files
Official URL
Full text at PDC
Publication Date
1988
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Matematisk Institut, Universitetsparken NY Munkegade
Abstract
Let S,q be the collection of all compact operators T on a (complex) Hilbert space H such that (INVALID INPUT),q(T) = (P1 n=1((n)sn(T))qn−1)1/q < 1.
Here (sn(T)) are the singular numbers of T, 0 < q 1 and :(0,1) ! (0,1) is a continuous function with (1) = 1 and ¯(t):= sups>0((ts)/(s)) < 1 for every t > 0.
The special case (t) = t1/p gives the operator space (Sp,q, p,q) introduced in 1967 by H. Triebel [Invent. Math. 4, 275-279 (1967; Zbl 0165.145)]. We characterize the dual of S,q. In particular, we prove that (Sp,q)0 = L(H) for 0 < p < 1 and 0 < q 1, or p = 1 and 0 < q < 1. This complements previous results of C. Merucci [C. R. Acad.
Sci., Paris, S´er. A 274, 1163-1166 (1972; Zbl 0238.46037)] and C. Gapaillard and Pham the Lai [Stud. Mat. 49, 129-138 (1974; Zbl 0244.47013)] on duality of Sp,q-spaces.