Related papers: Revisiting Operator $p$-Compact Mappings
We introduce the notion of regular operator mappings of several variables generalising the notion of spectral function. This setting is convenient for studying maps more general than what can be obtained from the functional calculus, and it…
In this note, we extend the definition of $p$-biharmonic and bi-$p$-harmonic maps between two Riemannian manifolds and explore some of their properties.
We will focus on studying the ball measure of non-compactness $\alpha(T)$ for various particular instances of embedding operators in sequence spaces. Our first main goal is to find necessary and sufficient conditions for an identity…
We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection…
The aim of this paper is to define and study $\mathcal{B}$-open sets and related properties. A $\mathcal{B}$-open set is, roughly speaking, a generalization of a $b$-open set, which is in turn a generalization of a pre-open set and a…
We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic…
Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic…
On the set of mappings of the given set, we define the product of mappings. If A is associative algebra, then we consider the set of matrices, whose elements are linear mappings of algebra A. In algebra of matrices of linear mappings we…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…
We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
In this paper, we first discussed multiplicative metric mapping by giving some topological properties of the relevant multiplicative metric space. As an interesting result of our discussions, we observed that the set of positive real…
This paper mainly concerns the von Neumann algebras induced by a tuple of multiplication operators on Bergman spaces which arise essentially from holomorphic proper maps over higher dimensional domains. We study the structures and abelian…
We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and…
Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient…
This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
We show that under natural and quite general assumptions, a large part of a matrix for a bounded linear operator on a Hilbert space can be preassigned. The result is obtained in a more general setting of operator tuples leading to…
To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a perfectoid analog of…