I recently completed my PhD at the Deparment of Mathematical & Statistical Sciences, Universiy of Alberta with the supervision
of  Dr. Vladimir Troitsky.


Research

My research interests are mainly in Functional Analysis and Operator Theory, in particular the invariant subspace problem. In my doctoral
research, I have been using the method of minimal vectors to find invariant subspaces and invariant order ideals for some classes of
bounded operators on ordered Banach spaces and Banach lattices.

I have also worked on a functional analytic model of Martingale Theoery. In this area of research, I am particularly interested in studying
the classical martingale theory from the perspective of Banach lattice theory.


Publications

1. Invariant subspaces of super-left Commutants,  Proc. of the Amer. Math. Soc., 137 (2009) 1357--1361.  PDF 

2. Invariant subspaces of positive quasinilpotent operators on ordered Banach spaces, with V. Troitsky. Positivity, 12 (2008), no. 2, 193--208. PDF

3. Martingales in Banach lattices II, with V. Troitsky. Positivity, to appear. PDF

4. Bounded indecomposable semigroups of non-negative matrices, with A.I.Popov, H.Radjavi, E.Spinu, and A.Tcaciuc, and V. Troitsky. Positivity, to appear. PDF
 
5. Invariant subspaces of positive operators & martingales in Banach lattices, PhD Thesis, 2009. PDF




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