Joint invariant subspaces for some commuting tuples of
bounded linear operators
J. Eschmeier used Scott Brown's technique in
J. reine angew. Math. 426(1992), 1-22, to prove the existence of some
joint invariant subspaces for certain commuting tuples that possess
decomposable extensions.
In the present paper we try to find the natural framework that allows
the application of these methods.
As remarked by M. Putinar, until now the only known way to obtain a
decomposable extension of the above type is to assume Bishop's
property.
The motivation for our work is that one can hope to obtain by other
means such extensions, as Corollary 2.2 in the present paper shows.