6 citations · 26 across the 19 of their papers we have counts for
8 papers · 1 filter
Invertibility of functions of operators and existence of hyperinvariant subspaces
Maria F. Gamal'
Let be an absolutely continuous polynomially bounded operator, and let be a singular inner function. It is shown that if is invertible and some additional conditions…
On existence of shift-type invariant subspaces for polynomially bounded operator
Maria F. Gamal'
A particular case of results from [K2] is as follows. Let the unitary asymptote of a contraction contain the bilateral shift (of finite or infinite multiplicity). Then there ex…
On polynomially bounded operators with shift-type invariant subspaces
Maria F. Gamal'
A particular case of [07] was generalized from contractions to polynomially bounded operators in [G19]. Namely, it is proved in [G19] that if the unitary asymptote of a polynomiall…
On contractions that are quasiaffine transforms of unilateral shifts
M. F. Gamal'
It is known that if is a contraction of class and is of trace class, then is a quasiaffine transform of a unilateral shift. Also it is known that if t…
Notes on the codimension one conjecture in the operator corona theorem
M. F. Gamal'
Answering on the question of S.R.Treil [23], for every , , examples of contractions are constructed such that their characteristic functions $F\in H^\infty(\mathcal E\to\…
On power bounded operators that are quasiaffine tranforms of singular unitaries
Maria F. Gamal'
In [9] a question is raised: if a power bounded operator is quasisimilar to a singular unitary operator, is it similar to this unitary operator? For polynomially bounded operators,…
A sufficient condition for the similarity of a polynomially bounded operator to a contraction
Maria Gamal'
Let be a polynomially bounded operator, and let be its invariant subspace. Suppose that is similar to a contraction, wh…
Examples of cyclic polynomially bounded operators that are not similar to contractions, II
Maria Gamal'
The question if polynomially bounded operator is similar to a contraction was posed by Halmos and was answered in the negative by Pisier. His counterexample is an operator of infin…