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Kernel maps and operator decomposition
Gabriel Matos, Lina Oliveira
We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and ke…
Weakly closed Lie modules of nest algebras
Lina Oliveira, Miguel Santos
Let be a nest algebra of operators on Hilbert space and let be a weakly closed Lie -module. We construct explicit…
A characterization of reflexive spaces of operators
Janko Bračič, Lina Oliveira
We show that for a linear space of operators the following assertions are equivalent. (i) is reflexive in the sense of…
Decomposability of bimodule maps
Christian Le Merdy, Lina Oliveira
Consider a unital C*-algebra A, a von Neumann algebra M, a unital sub-C*-algebra C of A and a unital *-homomorphism from C to M. Let u: A --> M be a decomposable map (i.e. a li…
Finite rank operators in Lie ideals of nest algebras
Lina Oliveira
The main theorem provides a characterisation of the finite rank operators lying in a norm closed Lie ideal of a continuous nest algebra. These operators are charaterised as those f…