Related papers: Linear maps preserving inner functions

We show that a sufficient condition for the weak limit of a sequence of $W^1_q$-homeomorphisms with finite distortion to be almost everywhere injective for $q \geq n-1$, can be stated by means of composition operators. Applying this result,…

We obtain a description of the homeomorphisms which induce bounded composition operators on Sobolev spaces of functions on metric measure spaces.

We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…

We prove that an arbitrary function, which is holomorphic on some neighbourhood of z=0 in $\mathbb{C}^N$ and vanishes at z=0, whose values are bounded linear operators mapping one separable Hilbert space into another one, can be represented…

It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in…

We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J.…

In this paper we introduce new spaces of holomorphic functions on the pointed unit disc of $\mathbb C$ that generalize classical Bergman spaces. We prove some fundamental properties of these spaces and their dual spaces. We finish the paper…

An implicit operation of a class of similar algebras $\mathsf{K}$ is a collection of first order definable partial functions on the members of $\mathsf{K}$ that is globally preserved by homomorphisms. For instance, "taking inverses" can be…

In this paper, first we characterize closedness of range of the finite sum of weighted composition operators between different Lp-spaces. Then we discuss polar decomposition and invertibility of these operators.

We characterize the analytic self-maps $\phi$ of the unit disk ${\Bbb D}$ in ${\Bbb C}$ that induce continuous composition operators $C_\phi$ from the log-Bloch space $\mathcal{B}^{\log}({\Bbb D})$ to $\mu$-Bloch spaces ${\mathcal…

Determining the range of complex maps plays a fundamental role in the study of several complex variables and operator theory. In particular, one is often interested in determining when a given holomorphic function is a self-map of the unit…

This paper considers homogeneous order preserving continuous maps on the normal cone of an ordered normed vector space. It is shown that certain operators of that kind which are not necessarily compact themselves but have a compact power…

The theme of the paper is the question of existence and basic structure of transfer operators for endomorphisms of a unital C*-algebra. We establish a complete description of non-degenerate transfer operators, characterize complete transfer…

Let $f$ be a holomorphic endomorphism of $\mathbb{P}^2$, let $T$ be its Green current and $\mu=T\wedge T$ be its equilibrium measure. We prove that if $\mu$ has a local product structure with respect to $T$ then (an iterate of) $f$…

We study a class of $\Z^{d}$-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of $\Z^{d}$. We prove that any measurable factor map and even…

We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar…

In this paper we initiate the study of real operator monotonicity for functions of tuples of operators, which are multivariate structured maps with a functional calculus called free functions that preserve the order between real parts (or…

Inner functions are the backbone of holomorphic function theory. This paper studies the inner functions on quotient domains of the open unit polydisc, $\bD^d$, arising from the group action of finite pseudo-reflection groups. Such quotient…

Let $X=(X,\mathcal{B},\mu)$ be a $\sigma$-finite measure space and \mbox{$f:X\to X$} be a measurable transformation such that the composition operator $T_f:\varphi\mapsto \varphi\circ f$ is a bounded linear operator acting on…

Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex…