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In this paper, we deal with three aspects of $p$-monotone operators. First we study $p$-monotone operators with a unique maximal extension (called pre-maximal), and with convex graph. We then deal with linear operators, and provide…
As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all…
The Lipschitz space of an infinite (locally-finite) graph is defined as the set of functions on the vertices of the graph such that the differences of the values between adjacent vertices remain bounded. In this paper we prove that this set…
This article is devoted to the stability of error bounds (local and global) for semi-infinite convex constraint systems in Banach spaces. We provide primal characterizations of the stability of local and global error bounds when systems are…
In a recent paper (2024) Camacho, C\'{a}novas, Mart\'{\i}nez-Legaz and Parra introduced bimonotone operators, i.e., operators $T$ such that both $T$ and $-T$ are monotone, and found some interesting applications to convex feasibility…
We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and…
Transfer operators and Ruelle zeta functions for super-continuous functions on one-sided topological Markov shifts are considered. For every super-continuous function, we construct a Banach space on which the associated transfer operator is…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of…
We generalize Loewner's method for proving that matrix monotone functions are operator monotone. The relation x \leq y on bounded operators is our model for a definition for C*-relations of being residually finite dimensional. Our main…
The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…
We give conditions for local diagonalization of analytic operator families acting between real or complex Banach spaces. The transformations are constructed from an operator Toeplitz matrix obtained from Jordan chains of increasing length.…
We give an extension of Rubio de Francia's extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an $m$-(sub)linear operator…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
A pointed convex cone naturally induces a partial order, and further a notion of nondecreasingness for functions. We consider extended real-valued functions defined on the cone. Monotone conjugates for these functions can be defined in an…
This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
A well-known result going back to the 1930s states that all bounded linear operators mapping scalar-valued $L^1$-spaces into $L^\infty$-spaces are kernel operators and that in fact this relation induces an isometric isomorphism between the…