Probabilistic Operator Algebra Seminar: Structure of operators on $L^p$ and $l^p$
Seminar | October 30 | 3:45-5:45 p.m. | 748 Evans Hall
March Boedihardjo, UCLA
I will present my recent results on operators on $L^p$ and $l^p$. These include (1) a characterization of the weak closure of ultrapowers of operators on $L^p$ and (2) $l^p$ versions of some results in the Brown-Douglas-Fillmore theory. Some applications will be shown: (1) ultrapowers of operators on $L^p$ have exactly 4 nontrivial invariant subspaces if the ultrafilter is selective (2) every unital homomorphism from C(M) into the Calkin algebra of $l^p$ can be expressed as a compression of a unital homomorphism from $C(M)$ into $B(l^p)$. Proofs of certain results are sketched. Some of the proofs are based on the proofs for Hilbert space and a probabilistic construction. However, the proof of homotopy invariance of the $Ext^-1$ group for $l^p$ uses an approach different from Kasparov's KK-theory.