Related papers: Exponential algebraicity in exponential fields

We give a criterion when a polynomial $x^n-g$ is irreducible over a pseudofinite field. As an application we give an explicit description of algebraic closure of some pseudofinite fields of zero characteristic.

We answer in the negative Siegel's question whether all E-functions are polynomial expressions in hypergeometric E-functions. Namely, we show that if an irreducible differential operator of order three annihilates an E-function in the…

Building over recent results, we expand the basic theory of algebraic extensions to the realm of superfields -a field with multivalued sum and product-, showing that every superfield has a (unique up to isomorphism) strong algebraic…

In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present…

In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space,…

We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…

Let $(K;+,\cdot, ', 0, 1)$ be a differentially closed field. In this paper we explore the connection between Ax-Schanuel type theorems (predimension inequalities) for a differential equation $E(x,y)$ and the geometry of the set $U:=\{…

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…

Let $X\subset\mathbb{R}^n$ be a convex closed and semialgebraic set and let $f$ be a polynomial positive on $X$. We prove that there exists an exponent $N\geq 1$, such that for any $\xi\in\mathbb{R}^n$ the function…

It is shown that the complex field equipped with the "approximate exponential map", defined up to ambiguity from a small group, is quasiminimal: every automorphism-invariant subset of the field is countable or co-countable. If the ambiguity…

We present an elementary Functional Analytic proof of the roughness of Exponential Dichotomy of Ordinary Differential Equations (with exponential growth) on an arbitrary Banach Space.

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…

We address special cases of the analogues of the exponential algebraic closedness conjecture relative to the exponential maps of semiabelian varieties and to the modular $j$ function. In particular, we show that the graph of the exponential…

Inspired by Conway's surreal numbers, we study real closed fields whose value group is isomorphic to the additive reduct of the field. We call such fields omega-fields and we prove that any omega-field of bounded Hahn series with real…

We affirmatively answer a conjecture in the preprint ``Essential dimension and algebraic stacks,'' proving that the essential dimension of an abelian variety over a number field is infinite.

All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C*-envelope.

Let $F$ be a fixed field of characteristic zero containing an element $i$ such that $i^2 = -1$. In this paper we consider finite dimensional superalgebras over $F$ endowed with a pseudoautomorphism $p$ and we investigate the asymptotic…

We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some…

We show that the essentially algebraic theory of generalized algebraic theories, regarded as a category with finite limits, has a universal exponentiable arrow in the sense that any exponentiable arrow in any category with finite limits is…

We prove that an arbitrary countable dimensional Lie algebra over a field of characteristic $\neq 2$ that is locally of subexponential growth is embeddable in a finitely generated Lie algebra of subexponential growth.