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Related papers: Approximation results on s-numbers of operators

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We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are additionally symmetric, then our results are optimal. For…

Numerical Analysis · Mathematics 2025-09-24 David Krieg , Erich Novak , Mario Ullrich

Let $X, Y$ be Banach spaces and $T : X \to Y$ be a bounded linear operator. In this paper, we initiate the study of the perturbation problems for bounded homogeneous generalized inverse $T^h$ and quasi--linear projector generalized inverse…

Functional Analysis · Mathematics 2013-02-19 Jianbing Cao , Yifeng Xue

We study the relationship between the residuality of the set of norm attaining functionals on a Banach space and the residuality and the denseness of the set of norm attaining operators between Banach spaces. Our first main result says that…

Functional Analysis · Mathematics 2023-02-02 Mingu Jung , Miguel Martin , Abraham Rueda Zoca

In the present article, we propose the generalization of Sz\'{a}sz-Mirakyan operators, which is a class of linear positive operators of discrete type depending on a real parameters. We give theorem of degree of approximation, the…

Classical Analysis and ODEs · Mathematics 2015-09-01 Prashantkumar Patel , Vishnu Narayan Mishra

Stochastic Approximation (SA) was introduced in the early 1950's and has been an active area of research for several decades. While the initial focus was on statistical questions, it was seen to have applications to signal processing,…

Statistics Theory · Mathematics 2024-02-28 Rajeeva Laxman Karandikar , Bhamidi V Rao

We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces…

Classical Analysis and ODEs · Mathematics 2015-05-18 Hannes Luiro , Antti V. Vähäkangas

In this paper, we study the boundedness of the Hilbert transformation in Lorentz function spaces, thereby complementing classical results of Boyd. We also characterize the optimal range of a triangular truncation operator in…

Functional Analysis · Mathematics 2021-01-11 F. Sukochev , K. Tulenov , D. Zanin

In this paper we study conditions on a Banach space X that ensure that the Banach algebra K(X) of compact operators is amenable. We give a symmetrized approximation property of X which is proved to be such a condition. This property is…

Functional Analysis · Mathematics 2008-02-03 Niels Gronbaek , Barry E. Johnson , George A. Willis

Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…

Optimization and Control · Mathematics 2026-02-03 Guillaume Lauga , Samuel Vaiter

This thesis addresses Pour-El and Richards' fourth question from their book "Computability in analysis and physics", concerning the relation between higher order recursion theory and computability in analysis. Among other things it is shown…

Logic · Mathematics 2012-07-30 Bjørn Kjos-Hanssen

We consider similarity transformations of a perturbed linear operator $A-B$ in a complex Banach space $\mathcal{X}$, where the unperturbed operator $A$ is a generator of a Banach $L_1(\mathbb{R})$-module and the perturbation operator $B$ is…

Functional Analysis · Mathematics 2024-04-02 Anatoly G. Baskakov , Ilya A. Krishtal , Natalia B. Uskova

We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We…

Functional Analysis · Mathematics 2021-07-23 T. Bottazzi , C. Conde , M. S. Moslehian , P. Wojcik , A. Zamani

Our objective in this paper is to present the sequence of Stancu type operators including generalized Brenke polynomials. We answer the problem of uniform approximation of continuous functions on closed bounded interval and the problem of…

Functional Analysis · Mathematics 2021-05-18 Sezgin Sucu

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

Optimization and Control · Mathematics 2020-08-31 Zheng Zhou , Bing Tan , Songxiao Li

In this paper, we firstly introduce nonlinear truncated Baskakov operators on compact intervals and obtain some direct theorems. Also, we give the approximation of fuzzy numbers by truncated nonlinear Baskakov operators.

General Mathematics · Mathematics 2023-12-04 Ecem Acar , Sevilay Kirci Serenbay , Saleem Yaseen Majeed Al Khalidy

We consider continuous Dirac operators defined on $\mathbf{R}^d$, $d\in\{1,2,3\}$, together with various discrete versions of them. Both forward-backward and symmetric finite differences are used as approximations to partial derivatives. We…

Mathematical Physics · Physics 2023-07-19 Horia D. Cornean , Henrik Garde , Arne Jensen

Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recently, the main idea behind existing SBP operators was that…

Numerical Analysis · Mathematics 2023-07-25 Jan Glaubitz , Simon-Christian Klein , Jan Nordström , Philipp Öffner

In this paper, we study the existence of the random fixed points for lower semicontinuous condensing random operators defined on Banach spaces. Our results extend corresponding ones present in literature.

Probability · Mathematics 2015-07-13 Monica Patriche

Basis of a Banach space with respect to a filter F on N (F-basis for short) is a generalization of basis, where the ordinary convergence of series is substituted by convergence of partial sums with respect to the filter F. We study the…

Functional Analysis · Mathematics 2025-09-25 V. Kadets , M. Manskova

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…

Spectral Theory · Mathematics 2019-02-19 Ruslan Sharipov