On the spectrum of the Sylvester-Rosenblum operator acting on triangular algebras
Abstract
Let A and B be algebras and M be an A -B-bimodule. For A ∈ A , B ∈B, we
define the Sylvester-Rosenblum operator τA,B :M →M via τA,B(M) = AM+MB for all M ∈
M . We investigate the spectrum of τA,B in three settings, namely: (a) when A = B = Tn(F) ,
the set of upper-triangular matrices over an algebraically closed field F and M ⊆ Mn(F); (b)
when A = B =M is a unital triangular Banach algebra; and (c), when M = T (N ) is the
nest algebra associated to a nest N on a complex, separable Hilbert space and A = B =
CI+K (N ) consists of the unitization of the algebra of compact operators in T (N ) .
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Cite this version of the work
Laurent Marcoux, Ahmed Ramzi Sourour
(2020).
On the spectrum of the Sylvester-Rosenblum operator acting on triangular algebras. UWSpace.
http://hdl.handle.net/10012/20317
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