M. Gamal’

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20242026

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math.FA2026

Non-stable subnormal contractions have nontrivial hyperinvariant subspaces

Maria F. Gamal'

A contraction $T$ on a (complex, separable) Hilbert space is stable, or of class $C_{0 \cdot}$ , if $T^{n} \to 0$ in the strong operator topology. It is proved that for a non-stable pur…

math.FA2025

Some relationships with subnormal operators and existence of hyperinvariant subspaces

Maria F. Gamal'

If $T$ is a polynomially bounded operator, $M$ is an invariant subspace of $T$ , $T ∣_{M}$ is a unilateral shift and $T^{*} ∣_{M^{⊥}}$ is subnormal, then $T…

math.FA2024

Examples of cyclic polynomially bounded operators that are not similar to contractions

Maria F. Gamal'

A question if a 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…

math.FA2024

On similarity to contractions of class $C_{\cdot 0}$ with finite defects

Maria F. Gamal'

A criterion on the similarity of a (bounded, linear) operator $T$ on a (complex, separable) Hilbert space $H$ in terms of shift-type invariant subspaces of $T$ to a contra…

Non-stable subnormal contractions have nontrivial hyperinvariant subspaces

Some relationships with subnormal operators and existence of hyperinvariant subspaces

Examples of cyclic polynomially bounded operators that are not similar to contractions

On similarity to contractions of class C⋅0​ with finite defects

On similarity to contractions of class $C_{\cdot 0}$ with finite defects