Related papers: On Exponential Factorizations of Matrices over Ban…

We present new completeness conditions for exponential systems on the complex plane in Banach algebras of continuous functions on a compact with a connected complement that are simultaneously holomorphic in the interior of this compact if…

We characterize the holomorphic mappings $f$ between complex Banach spaces that may be written in the form $f=T\circ g$, where $g$ is another holomorphic mapping and $T$ belongs to a closed surjective operator ideal.

In this paper, we investigate whether the tensor product of two frames, each individually localised with respect to a spectral matrix algebra, is also localised with respect to a suitably chosen tensor product algebra. We provide a partial…

We give a new scale of completeness conditions for exponential systems in two types of functional spaces on subsets of the complex plane. The first is the Banach spaces of functions that are continuous on a compact and simultaneously…

Suppose B is the unital algebra consisting of the algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and…

A factorization of the inverse of a Hermetian positive definite matrix based on a diagonal by diagonal recurrence formulae permits the inversion of Block Toeplitz matrices, using only matrix-vector products, and with a complexity of…

Let $V$ be a vector space with countable dimension over a field, and let $u$ be an endomorphism of it which is locally finite, i.e. $(u^k(x))_{k \geq 0}$ is linearly dependent for all $x$ in $V$. We give several necessary and sufficient…

Let $D$ be the ring of integers of a quadratic number field $\mathbb{Q}[\sqrt{d}]$. We study the factorizations of $2 \times 2$ matrices over $D$ into idempotent factors. When $d < 0$ there exist singular matrices that do not admit…

In this survey paper we study parametric versions of writing a matrix in $SL_n (\mathbb{C})$ as a product of lower and upper unitriangular matrices in interchanging order as well as generalizations to other classical groups. We give an…

We are able to explicitly compute the bimodule structure of von Neumann algebra inclusions in handle constructions, which arise as inductive limits of iterated amalgamated free products not elementarily equivalent to $L(\mathbb{F}_2)$. Our…

We introduce multi-sheeted versions of algebraic domains and quadrature domains, allowing them to be branched covering surfaces over the Riemann sphere. The two classes of domains turn out to be the same, and the main result states that the…

A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach…

A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a…

We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…

We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M…

Let $(M,\Gamma)$ be a Hopf--von Neumann algebra, so that $M_\ast$ is a completely contractive Banach algebra. We investigate whether the product of two elements of $M$ that are both weakly almost periodic functionals on $M_\ast$ is again…

The well-known factorization theorem of Lozanovski{\u \i} may be written in the form $L^{1}\equiv E\odot E^{\prime}$, where $\odot $ means the pointwise product of Banach ideal spaces. A natural generalization of this problem would be the…

We prove an explicit integral formula for computing the product of two shifted Riemann zeta functions everywhere in the complex plane. We show that this formula implies the existence of infinite families of exact exponential sum identities…

The fully matricial generalization in part I, of the difference quotient derivation on holomorphic functions, in which ${\mathbb C}$ is replaced by a Banach algebra $B$, is extended from the affine case to a Grassmannian completion. The…

The purpose of this article is to show that Theorems 2.2-2.5 from [1] apply to the product of random matrices considered by Grama, Le Page, and Peign\'e [2]. This allows us, in particular, to emphasize the general nature of the formulation…