6 papers · 1 filter
On interplay between operators, bases, and matrices
Vladimir Müller, Yuri Tomilov
Given a bounded linear operator on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for having certain specified algebraic…
In search of convexity: diagonals and numerical ranges
Vladimir Müller, Yuri Tomilov
We show that the set of all possible constant diagonals of a bounded Hilbert space operator is always convex. This, in particular, answers an open question of J.-C. Bourin ()…
Invariant half-spaces for rank-one perturbations
Vladimir Muller
If T is a bounded linear operator acting on an infinite-dimensional Banach space, then there exists and operator F of rank at most one and arbitrarily small norm such that T-F has…
High order isometric liftings and dilations
Catalin Badea, Vladimir Müller, Laurian Suciu
We show that a Hilbert space bounded linear operator has an -isometric lifting for some integer if and only if the norms of its powers grow polynomially. In analogy wit…
Power bounded operators and the mean ergodic theorem for subsequences
Tanja Eisner, Vladimir Müller
Let be a power bounded Hilbert space operator without unimodular eigenvalues. We show that the subsequential ergodic averages converge in the stron…
Diagonals of operators and Blaschke's enigma
Vladimir Muller, Yuri Tomilov
We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framew…