Related papers: Choquet operators associated to vector capacities
We investigate integral representation of vector-valued function spaces, i.e., of subspaces $H\subset C(K,E)$, where $K$ is a compact space and $E$ is a (real or complex) Banach space. We point out that there are two possible ways of…
In this paper we provide a unifying approach to the study of Banach ideals of linear and multilinear operators defined, or characterized, by the transformation of vector-valued sequences. We investigate and apply the linear and multilinear…
In this paper, we study vector valued de Branges spaces associated with a de Branges operator, defined as a pair of Fredholm operator valued analytic functions on a domain symmetric with respect to the unit circle. Using a suitable direct…
The purpose of this article is to present the construction and basic properties of the general Bochner integral. The approach presented here is based on the ideas from the book The Bochner Integral by J. Mikusinski where the integral is…
In his influential work Choquet systematically studied capacities on Boolean algebras in a topological space, and gave a probabilistic interpretation for completely monotone (and completely alternating) capacities. Beyond complete…
We establish a dilation-theoretic characterization of the Choquet order on the space of measures on a compact convex set using ideas from the theory of operator algebras. This yields an extension of Cartier's dilation theorem to the…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
We study the effective potential for composite operators. Introducing a source coupled to the composite operator, we define the effective potential by a Legendre transformation. We find that in three or fewer dimensions, one can use the…
This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.
We develop a completely bounded counterpart to the non-commutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we…
It is well known that iterates of quasi-compact operators converge towards a spectral projection, whereas the explicit construction of the limiting operator is in general hard to obtain. Here, we show a simple method to explicitly construct…
We construct an infinite dimensional Banach space of continuous functions C(K) such that every one-to-one operator on C(K) is onto.
We study the space of vector-valued (twisted) conjugate invariant functions on a connected reductive group.
A vector partition function is the number of ways to write a vector as a non-negative integer-coefficient sum of the elements of a finite set of vectors $\Delta$. We present a new algorithm for computing closed-form formulas for vector…
In this paper, we define several types of maximal operators on sequence spaces occuring in Harmonic analysis and present various connections between them.
A Markov operator $P$ acting on $C(X)$, where $X$ is compact, gives rise to a natural topological quiver. We use the theory of such quivers to attach a $C^{*}$-algebra to $P$ in a fashion that reflects some of the probabilistic properties…
The inverse of an $\infty \times \infty$ symmetric band matrix can be constructed in terms of a matrix continued fraction. For Hamiltonians with Coulomb plus polynomial potentials, this results in an exact and analytic Green's operator…
Quantum Iterated Function System on a complex projective space is defined by a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
In this paper we characterize multiplication operators induced by operator valued maps on Banach function spaces. We also study multiplication semigroups and stability of these operators.