Abstract
Abstract
In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair
$\mathbf {T}=(T_{1},T_{2})$
and investigate nontrivial invariant subspaces between the generalized spherical Aluthge transform of the linear pencil of
$\mathbf {T}$
and the linear pencil of the original pair
$\mathbf {T}$
of bounded operators with dense ranges.
Publisher
Canadian Mathematical Society