Lina Oliveira

Normalisers of operator algebras and tensor product formulas

We establish a tensor product formula for bimodules over maximal abelian selfadjoint algebras and their supports. We use this formula to show that if A is the tensor product of finitely many continuous nest algebras, B is a CSL algebra and A and B have the same normaliser semi-group then either A = B or A∗ = B. We show that the result does not hold without the assumption that the nests be continuous, answering in the negative a question raised in [28].

Image reconstruction based on circulant matrices

Abstract We propose a new method for image reconstruction based on circulant matrices. The novelty of this method is the image treatment using a simple and classical algebraic structure, the circulant matrix, which significantly reduces the computational effort, nevertheless providing reliable outputs. We compare the results with well established techniques such as the Principal Component Analysis (PCA) and the Discrete Fourier Transform (DFT), and the recently introduced Randomized Singular Value Decomposition (RSVD). We conclude that the quality is comparable whilst the computational time is considerably reduced.

A characterization of reflexive spaces of operators

We show that for a linear space of operators M ⊆ B(H1, H2) the following assertions are equivalent. (i) M is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map Ψ = (ψ1, ψ2) on a bilattice Bil(M) of subspaces determined by M with P ≤ ψ1(P,Q) and Q ≤ ψ2(P,Q) for any pair (P,Q) ∈ Bil(M), and such that an operator T ∈ B(H1, H2) lies in M if and only if ψ2(P,Q)Tψ1(P,Q) = 0 for all (P,Q) ∈ Bil(M). This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces.

Decomposability of Bimodule Maps

Consider a unital C*-algebra A, a von Neumann algebra M, a unital sub-C*-algebra C of A and a unital *-homomorphism

On the structure of inner ideals of nest algebras

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Weak*-closed Jordan ideals of nest algebras

from C to M. Let u: A --> M be a decomposable map (i.e. a linear combination of completely positive maps) which is a C-bimodule map with respect to

Finite rank operators in Lie ideals of nest algebras

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A decomposition theorem for Lie ideals in nest algebras

. We show that u is a linear combination of C-bimodule completely positive maps if and only if there exists a projection e in the commutant of

On range tripotents in JBW*-triples

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Tits–Kantor–Koecher Lie algebras of JB*-triples

such that u is valued in eMe and