Related papers: On Some Estimates for Projection Operator in Banac…

We present an overview to the approximation property, paying especial attention to the recent results relating the approximation property to ideals of linear operators and Lipschitz ideals. We complete the paper with some new results on…

Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists…

In this work, we develop the discrete solvability analysis for perturbed saddle-point problems in Banach spaces with forcing terms regularised by means of a projector constructed using the adjoint of a weighted Cl\'ement…

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a…

Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…

We study the boundedness of averaging projections associated with symmetric Schauder bases in quasi-Banach spaces. Although this property is standard in the Banach setting, it is far from clear in the absence of local convexity and, indeed,…

Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…

We develop and analyse numerical schemes for uncertainty quantification in neural field equations subject to random parametric data in the synaptic kernel, firing rate, external stimulus, and initial conditions. The schemes combine a…

Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…

The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…

We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…

The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can…

We investigate the space of bounded linear operators on a Banach space equipped with a norm which is equivalent to the operator norm such that the subspace of compact operators is an M-ideal. In particular, we observe that the space of…

We introduce a weakened notion of norm attainment for bounded linear operators between Banach spaces which we call \emph{quasi norm attaining operators}. An operator $T\colon X \longrightarrow Y$ between the Banach spaces $X$ and $Y$ is…

We present explicit expressions for Fock-space projection operators that correspond to realistic final states in scattering experiments. Our operators automatically sum over unobserved quanta and account for non-emission into sub-regions of…

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence…

This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…

For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral…

We show examples of compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. This is the negative answer to an open question posed in the 1970's. Actually, any strictly convex Banach space…