M. Gamal’

collaborators

6 papers

math.FA2018

Invertibility of functions of operators and existence of hyperinvariant subspaces

Maria F. Gamal'

Let $T$ be an absolutely continuous polynomially bounded operator, and let $θ$ be a singular inner function. It is shown that if $θ (T)$ is invertible and some additional conditions…

math.FA2018

On contractions that are quasiaffine transforms of unilateral shifts

M. F. Gamal'

It is known that if $T$ is a contraction of class $C_{10}$ and $I - T^{*} T$ is of trace class, then $T$ is a quasiaffine transform of a unilateral shift. Also it is known that if t…

math.FA2018

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 $δ$ , $0 < δ < 1$ , examples of contractions are constructed such that their characteristic functions $F\in H^\infty(\mathcal E\to\…

math.FA2018

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,…

math.FA2018

A sufficient condition for the similarity of a polynomially bounded operator to a contraction

Maria Gamal'

Let $T$ be a polynomially bounded operator, and let $M$ be its invariant subspace. Suppose that $P_{M^{⊥}} T ∣_{M^{⊥}}$ is similar to a contraction, wh…

math.FA2018

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…