8,910 research outputs found
The Fine Structure of the Kasparov Groups II: topologizing the UCT
The Kasparov groups KK_*(A, B) have a natural structure as pseudopolonais
groups. In this paper we analyze how this topology interacts with the terms of
the Universal Coefficient Theorem (UCT) and the splittings of the UCT
constructed by J. Rosenberg and the author, as well as its canonical three term
decomposition which exists under bootstrap hypotheses. We show that the various
topologies on Ext_{\Bbb Z}^1(K_*(A), K_*(B)) and other related groups mostly
coincide. Then we focus attention on the Milnor sequence and the fine structure
subgroup of KK_*(A, B).
An important consequence of our work is that under bootstrap hypotheses the
closure of zero of KK_*(A, B) is isomorphic to the group Pext_{\Bbb
Z}^1(K_*(A), K_*(B)).
Finally, we introduce new splitting obstructions for the Milnor and Jensen
sequences and prove that these sequences split if K_*(A) or K_*(B) is torsion
free.Comment: 25 page
The mathematical research of William Parry FRS
In this article we survey the mathematical research of the late William (Bill) Parry, FRS
Transference in spaces of measures
The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a
powerful tool with many applications to singular integrals, ergodic theory, and
spectral theory of operators. Transference methods afford a unified approach to
many problems in diverse areas, which before were proved by a variety of
methods. The purpose of this paper is to bring about a similar approach to the
study of measures. Specifically, deep results in classical harmonic analysis
and ergodic theory, due to Bochner, de Leeuw-Glicksberg, Forelli, and others,
are all extensions of the classical F.&M. Riesz Theorem. We will show that all
these extensions are obtainable via our new transference principle for spaces
of measures.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints
- …