Related papers: Dilation theory in finite dimensions and matrix co…
In the study of open quantum systems, one commonly describes the evolution of a system of interest through reduced dynamics, obtained by treating the environment indirectly rather than as a part of the full model. This thesis presents an…
In representation theory of graded Iwanaga-Gorenstein algebras, tilting theory of the stable category $\underline{\mathsf{CM}}^{\mathbb{Z}} A$ of graded Cohen-Macaulay modules plays a prominent role. In this paper we study the following two…
Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations,…
We prove a stability theorem for finite-dimensional analytic inverse problems. Let \(U\subset\R^m\) be an open parameter set, let \(F(p)\) be a boundary measurement operator, and let \(R(p)\) be the finite-dimensional quantity to be…
We prove a local convex version of Arveson's extension theorem and of Wittstock's extension theorem. Also we prove a Stinespring type theorem for unbounded local completely contractive maps.
Diversities are an extension of the concept of a metric space which assign a non-negative value to every finite set of points, rather than just pairs. A general theory of diversities has been developed which exhibits many deep analogies to…
In this article we study convexity properties of distance functions in infinite dimensional Finsler unitary groups, such as the full unitary group, the unitary Schatten perturbations of the identity and unitary groups of finite von Neumann…
We prove a dynamical Shafarevich theorem on the finiteness of the set of isomorphism classes of rational maps with fixed degeneracies. More precisely, fix an integer d at least 2 and let K be either a number field or the function field of a…
The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of…
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…
We prove a version of the Poincar\'e-Bendixson theorem for certain classes of curves on the 2-sphere which are not required to be the trajectories of an underlying flow or semiflow on the sphere itself. Using this result we extend the…
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
This paper examines actions of right LCM semigroups by endomorphisms of C*-algebras that encode an additional structure of the right LCM semigroup. We define contractive covariant representations for these semigroup dynamical systems and…
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential…
A very general KSGNS type dilation theorem in the context of right (not necessarily Hilbert) modules over $C^*$-algebras is presented. The proof uses Kolmogorov type decompositions for positive-definite kernels with values in spaces of…
We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
We establish dilation theorems for non-tight frames with additional structure, i.e., frames generated by unitary groups of operators and projective unitary representations. This generalizes previous dilation results for Parseval frames due…