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Boudi, Nadia; Bračič, Janko (2013)
Languages: English
Types: Preprint
Subjects: Mathematics - Operator Algebras, Mathematics - Functional Analysis

Classified by OpenAIRE into

arxiv: Mathematics::Functional Analysis, Mathematics::General Topology
Let $\mathscr{X}$ be a complex Banach space and $\mathcal{L}(\mathscr{X})$ be the algebra of all bounded linear operators on $\mathscr{X}$. For a given elementary operator $\Phi$ of length $2$ on $\mathcal{L}(\mathscr{X})$, we determine necessary and sufficient conditions for the existence of a solution of the equation ${\rm X} \Phi=0$ in the algebra of all elementary operators on $\mathcal{L}(\mathscr{X})$. Our approach allows us to characterize some invertible elementary operators of length $2$ whose inverses are elementary operators.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • Write Ψ = P2 i=1 MAi,Bi, where Ai ∈ L(Ψ) and Bi ∈ R(Ψ). Then there exist E1, . . . , En ∈ U and F1, . . . , Fn ∈ V such that
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