Related papers: Matrix-Valued Corona Theorem for Multiply Connecte…

In this paper we extend a method of Arveson and McCullough to prove a tangential interpolation theorem for subalgebras of $H^\infty$. This tangential interpolation result implies a Toelitz corona theorem. In particular, it is shown that the…

This paper addresses the Corona problem for slice hyperholomorphic functions for a single quaternionic variable. While the Corona problem is well-understood in the context of one complex variable, it remains highly challenging in the case…

The corona problem was motivated by the question of the density of the open unit disc in the maximal ideal space of the algebra of bounded holomorphic functions on the unit disc. The corona problem connects operator theory, function theory,…

We continue our exposition concerning the Caratheodory topology for multiply connected domains by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of…

We construct a corona of a relatively hyperbolic group by blowing-up all parabolic points of its Bowditch boundary. We relate the $K$-homology of the corona with the $K$-theory of the Roe algebra, via the coarse assembly map. We also…

We prove that the multiplier algebra of the Drury-Arveson Hardy space $H_{n}^{2}$ on the unit ball in $\mathbb{C}^{n}$ has no corona in its maximal ideal space, thus generalizing the famous Corona Theorem of L. Carleson to higher…

The corona factorization property is a property with connections to extension theory, K-theory and the structure of C*algebras. This paper is a short survey of the subject, together with some new results and open questions.

In the paper we prove an extension theorem for matrices with entries in H^{\infty}(U) for U being a Riemann surface of a special type. One of the main components of the proof is a Grauert type theorem for "holomorphic" vector bundles…

A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed curve is presented. It is based on the application of the residual theorem. The quadrature is performed by evaluating the principal argument…

Courant's theorem implies that the number of nodal domains of a Laplace eigenfunction is controlled by the corresponding eigenvalue. Over the years, there have been various attempts to find an appropriate generalization of this statement in…

For $G$-monogenic mappings taking values in the algebra of complex quaternion we prove a curvilinear analogue of the Cauchy integral theorem in the case where a curve of integration lies on the boundary of a domain.

We study the $H^{\infty}(\mathbb{B}_{n})$ Corona problem $\sum_{j=1}^{N}f_{j}g_{j}=h$ and show it is always possible to find solutions $f$ that belong to $BMOA(\mathbb{B}_{n})$ for any $n>1$, including infinitely many generators $N$. This…

We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…

We give a short proof of the following theorem of Hara and Nakai: for a finitely bordered Riemann surface $R$, one can find an upper bound of the corona constant of $R$ that depends only on the genus and the number of boundary components of…

The solvability of the Riemann-Hilbert boundary value problem on the real line is described in the case when its matrix coefficient admits a Wiener-Hopf type factorization with bounded outer factors but rather general diagonal elements of…

Assume that $A$ is a closed linear operator defined on all of a Hilbert space $H$. Then $A$ is bounded. A new short proof of this classical theorem is given on the basis of the uniform boundedness principle. The proof can be easily extended…

In this paper, we prove the corona theorem for $M(D(\mu_k))$ in two different ways, where $\mu_k = \sum_{i=1}^k a_i \delta_{\zeta_i}$. Then we prove that the Bass stable rank of $M(D(\mu_k))$ is one.

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the…

In the present paper continuing our previous work we prove an extension theorem for matrices with entries in the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of…

The interpolating sequences for $H^{\infty}({\mathbb{D}}),$ the bounded holomorphic function in the unit disc ${\mathbb{D}}$ of the complex plane ${\mathbb{C}},$ {\small where characterised by L. Carleson by metric conditions on the points.…