Full paper in PDF format:
$%R. Kerman, M. Milman, and G. Sinnamon, On the Brudnyĭ-Krugljak duality theory of spaces formed by the K-method of interpolation, Rev. Mat. Complut. 20 (2007), no. 2, 367–389.%$

On the Brudnyĭ-Krugljak Duality Theory of Spaces Formed by the K-Method of Interpolation
Ron KERMAN, Mario MILMAN,
and Gord SINNAMON
Department of Mathematics
Brock University
St. Catharines
Ontario L2S 3A1 — Canada
rkerman@brocku.ca
Department of Mathematics
Florida Atlantic University
Boca Raton, Florida 33431 — USA
milman@fau.edu
Department of Mathematics
University of Western Ontario
London, Ontario
L6A 5B7 — Canada
sinnamon@uwo.ca

Received: August 9, 2006
Accepted: January 22, 2007

ABSTRACT

The Brudnyĭ-Krugljak duality theory for the K-method is elaborated for a class of parameters derived from rearrangement-invariant spaces. As examples, concrete expressions are given for the norms dual to certain interpolation spaces between two rearrangement-invariant spaces. These interpolation spaces are formed by the K-method using parameters related to classical Lorentz spaces or Orlicz spaces.

Key words: interpolation spaces, rearrangement-invariant spaces, Lorentz spaces, Orlicz spaces, duality.
2000 Mathematics Subject Classification: 46B70, 46E30.