Related papers: Weak and strong convergence theorems for enriched …
We establish a framework for weak and strong convergence of matrix models to operator-valued semicircular systems parametrized by operator-valued covariance matrices $\eta = (\eta_{i,j})_{i,j \in I}$. Non-commutative polynomials are…
We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint…
We establish a weighted version of the $H^p$-theory of quasiconformal mappings.
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…
We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalised convergence proofs along with explicit rates of convergence. More…
Using a Hilbert space framework inspired by the methods of orthogonal projections and Hodge decompositions, we study a general class of problems (called Z-problems) that arise in effective media theory, especially within the theory of…
In this paper, we presented a new type of metric space called $(\alpha,\beta)$-metric space along with some novel contraction mappings named $(\alpha,\beta)$-contraction and weak $(\alpha,\beta)$-contraction mapping. We established some…
We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…
The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…
We prove that for every semigroup of Schwarz maps on the von~Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space…
A family of random matrices is said to converge strongly to a limiting family of operators if the operator norm of every noncommutative polynomial of the matrices converges to that of the limiting operators. Recent developments surrounding…
The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…
We study the convergence analysis of a Picard-S iteration method for a particular class of weak-contraction mappings. Furthermore, we prove a data dependence result for fixed point of the class of weak-contraction mappings with the help of…
The purpose of this paper is to characterize weak supercyclicity for Hilbert-space contractions, which is shown to be equivalent to characterizing weak supercyclicity for unitary operators$.$ This is naturally motivated by an open question…
We investigate if an existing notion of weak sequential convergence in a Hadamard space can be induced by a topology. We provide an answer on what we call weakly proper Hadamard spaces. A notion of dual space is proposed and it is shown…
We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…
Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…
In 2008, J. Parcet showed the $(1,1)$ weak-boundedness of Calder\'on-Zygmund operators acting on functions taking values in a von Neumann algebra. We propose a simplified version of his proof using the same tools : Cuculescu's projections…
We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…
Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the…