Related papers: Regular Sequences of Quasi-Nonexpansive Operators …

These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…

We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost-orthogonality relations. This result is…

Many recently proposed gradient projection algorithms with inertial extrapolation step for solving quasi-variational inequalities in Hilbert spaces are proven to be strongly convergent with no linear rate given when the cost operator is…

This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fej\'er monotonicity, which is thoroughly…

In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…

Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.

This paper advances the study of multivariate function approximation using neural network operators activated by symmetrized and perturbed hyperbolic tangent functions. We propose new non-linear operators that preserve dynamic symmetries…

In 2012 G\u{a}vru\c{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this…

We study random iterations of averaged operators in Hilbert spaces and prove that the associated residuals converge exponentially fast, both in expectation and almost surely. Our results provide quantitative bounds in terms of a single…

In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of…

Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation operators used in…

Quasiperiodic arrangements of the constitutive materials in composites result in effective properties with very unusual electromagnetic and elastic properties. The paper discusses the cut-and-projection method that is used to characterize…

We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of associated (semi-)groups, (essential) spectra and spectral…

Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…

This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…

Given a finite collection $\mathbf{V}:=(V_1,\dots,V_N)$ of closed linear subspaces of a real Hilbert space $H$, let $P_i$ denote the orthogonal projection operator onto $V_i$ and $P_{i,\lambda}:= (1-\lambda)I + \lambda P_i$ denote its…

This paper is to study some conditions on semigroups, generated by some class of non-densely defined operators in the closure of its domain, in order that certain bounded perturbations preserve some regularity properties of the semigroup…

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…

For a linear nonvariational operator structured on smooth H\"ormander's vector fields, with H\"older continuous coefficients, we prove a regularity result in the spaces of H\"older functions. We deduce an analogous regularity result for…

Let $A$ be an unbounded operator on a Banach space $X$. It is sometimes useful to improve the operator $A$ by extending it to an operator $B$ on a larger Banach space $Y$ with smaller spectrum. It would be preferable to do this with some…