Raymond Lubansky, PhD
Thesis: "Axiomatic spectral theory" -- Degree granted 2008
Supervisor: Associate Professor J. J. Koliha
Publications:
Koliha-Drazin invertibles form a regularity - available online at the Mathematical Proceedings of the Royal Irish Academy
Research announcement: g-Kato operators form a regularity
introduces the g-Kato operators, investigates some of their properties
and proves that they form a regularity in the sense of Muller
Alegra Dajic
Supervisor: Associate Professor J. J. Koliha
Thesis: "Generalized Operator Inverses with Applications"
Publications:
Positive solutions to the equations $AX=C$ and $XB=D$ for Hilbert space operators, Journal of Mathematical nalysis and Applications 333 (2007), 567--576 (with J. J. Koliha)
The weighted $g$-Drazin inverse for operators, Journal of Australian Mathematical Society 82 (2007), 163--181 (with J. J. Koliha)
The $\sigma g$-Drazin inverse and the generalized Mbekhta decomposition, Integral Equations and Operator Theory 57 (2007), 309--326 (with J. J. Koliha)
The weighted $g$-Drazin inverse for operators, Journal of the Australian Mathematical Society 81 (2006), 405--423 - corrected printing (with J. J. Koliha)
Positive and real-positive solutions to the equation axa*=c in C*-algebras, Linear and Multilinear Algebra 55, 535--543 (with D. Cvetkovic and J. J. Koliha)
Equations ax=c and xb=d in rings and rings with involution with applications to Hilbert space operators, Linear Algebras and its Applications (online) (with J. J. Koliha)
Daniel Grixti-Cheng
Supervisor: Associate Professor J. J. Koliha
Thesis: "Functional Analysis for Multivalued Linear Relations"
Publications:
The invariant subspace problem for bounded linear relations on Hilbert spaces, Australian Journal of Mathematical Analalysis and Applications 5 (2008), no. 1, Art. 4, 7 pp.