Stanislav Shkarin

most citedHypercyclic tuples of operators on

C^{n}

and

R^{n}

3 citations · 5 across the 6 of their papers we have counts for

collaborators

6 papers

math.FA2010★ 1 cited

A complete locally convex space of countable dimension admitting an operator with no invariant subspaces

Stanislav Shkarin

We construct a complete locally convex topological vector space $X$ of countable algebraic dimension and a continuous linear operator $T : X \to X$ such that $T$ has no non-trivial cl…

math.FA2010

A hypercyclic finite rank perturbation of a unitary operator

Stanislav Shkarin

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space $\H$ are constructed such that $V + R$ is hypercyclic. This answers affirmatively a question of Salas whe…

math.FA2010

On orbits of truncated convolution operators

Stanislav Shkarin

We prove that a semigroup generated by a finitely many truncated convolution operators on $L^{p} [0, 1]$ with $1 \leq p < \infty$ is non-supercyclic. On the other hand, there is a truncat…

math.DS2010★ 3 cited

Hypercyclic tuples of operators on $C^{n}$ and $R^{n}$

Stanislav Shkarin

A tuple $(T_{1}, \dots, T_{n})$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x \in X$ such that the the orbit of $x$ under the actio…

math.FA2010★ 1 cited

Chaotic Banach algebras

Stanislav Shkarin

We construct an infinite dimensional non-unital Banach algebra $A$ and $a \in A$ such that the sets $\{za^n:z\in\C,\ n\in\N\}$ and ${(1 + a)^{n} a : n \in N}$ are both dense in $A$ ,…

math.RA2010

The Golod-Shafarevich inequality for Hilbert series of quadratic algebras and the Anick conjecture

Natalia Iyudu, Stanislav Shkarin

We study the question on whether the famous Golod-Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question w…

A complete locally convex space of countable dimension admitting an operator with no invariant subspaces

A hypercyclic finite rank perturbation of a unitary operator

On orbits of truncated convolution operators

Hypercyclic tuples of operators on Cn and Rn

Chaotic Banach algebras

The Golod-Shafarevich inequality for Hilbert series of quadratic algebras and the Anick conjecture

Hypercyclic tuples of operators on $C^{n}$ and $R^{n}$