Extensions of linear operators from hyperplanes and strong uniqueness of best approximation in L(X,W)

2019 ◽  
Vol 246 ◽  
pp. 28-42
Author(s):  
Paweł Wójcik
Keyword(s):  
Best Approximation ◽  
Linear Operators ◽  
Strong Uniqueness ◽  
Uniqueness Of Best Approximation

Best approximation in L(X, Y)

1988 ◽  
Vol 104 (3) ◽  
pp. 527-531 ◽  
Author(s):  
W. Deeb ◽  
R. Khalil
Keyword(s):  
Banach Spaces ◽  
Best Approximation ◽  
Related Problem ◽  
Closed Subspace ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear

AbstractLet X, Y be Banach spaces and G a closed subspace of Y. Let L(X, Y) be the space of bounded linear operators from X into Y. In this paper we investigate when L(X, G) is proximal in L(X, Y). Further, we discuss the related problem of proximinality of L∞(T, G) in L∞(T, Y). We improve results obtained by Light and Cheney in this direction.

An extension of the method of the hypercircle to linear operator problems with unilateral constraints

1980 ◽  
Vol 85 (3-4) ◽  
pp. 173-193 ◽  
Author(s):  
W. D. Collins
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Boundary Value Problems ◽  
Best Approximation ◽  
Decomposition Theorem ◽  
Linear Operators ◽  
Unilateral Constraints ◽  
Abstract Boundary ◽  
Polar Cones ◽  
Approximation Problems

SynopsisBy using a Hilbert space decomposition theorem for two polar cones it is shown that the method of the hypercircle can be extended to determine solutions to best approximation problems involving unilateral constraints. The method is applied to abstract boundary value problems for linear operators involving such constraints.

Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol'skii-Besov spaces

2020 ◽  
Vol 17 (3) ◽  
pp. 372-395
Author(s):  
Anatolii Romanyuk ◽  
Viktor Romanyuk
Keyword(s):  
Besov Spaces ◽  
Best Approximation ◽  
Linear Operators ◽  
Trigonometric Polynomials ◽  
Exact Order ◽  
Periodic Functions ◽  
Sobolev Classes ◽  
The Best Approximation ◽  
Several Variables

We have obtained the exact-order estimates for some approximative characteristics of the Sobolev classes $\mathbb{W}^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}$ and Nikоl'skii--Besov classes $\mathbb{B}^{\boldsymbol{r}}_{p,\theta}\ $ of periodic functions of one and several variables in the norm of the space $B_{\infty, 1}$. Properties of the linear operators realizing the orders of the best approximation for the classes $\mathbb{B}^{\boldsymbol{r}}_{\infty, \theta}$ in this space by trigonometric polynomials generated by a set of harmonics with $``$numbers$"$ from step hyperbolic crosses are investigated.

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