10 papers
Invariant subspaces for operators with spectrum containing the boundary of the numerical range
Vladimir Müller, Yuri Tomilov
We prove that a bounded Hilbert space operator has a nontrivial invariant subspace whenever its spectrum contains the topological boundary of its numerical range. We also give vari…
Real linear operators and numerical ranges
Damian Kołaczek, Vladimir Müller
Real linear operators between two complex Banach spaces unify naturally two important classes of linear operators and antilinear operators. We give a survey of basic geometric, spe…
Interior Hölder continuity for singular-degenerate porous medium type equations with an application to a biofilm model
V. Hissink Muller
We show interior Hölder continuity for a class of quasi-linear degenerate reaction-diffusion equations. The diffusion coefficient in the equation has a porous medium type degenerac…
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…