Related papers: Best approximation in spaces of compact operators
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under…
Answering in the affirmative a question posed in [Y.A.Abramovich, C.D.Aliprantis and O.Burkinshaw, Multiplication and compact-friendly operators, Positivity 1 (1997), 171--180], we prove that a positive multiplication operator on any…
For a class of de Branges spaces containing polynomials, sufficient and necessary conditions are given for the boundedness and compactness of the Hausdorff operators under consideration. For the Paly-Wiener spaces we reduce the study of our…
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
Let $H_1, H_2$ be complex Hilbert spaces and $T$ be a densely defined closed linear operator from its domain $D(T)$, a dense subspace of $H_1$, into $H_2$. Let $N(T)$ denote the null space of $T$ and $R(T)$ denote the range of $T$. Recall…
We define and discuss properties of the class of unbounded operators which attain minimum modulus. We establish a relationship between this class and the class of norm attaining bounded operators and compare the properties of both. Also we…
In this paper, we introduce the concept of cyclic orbital contraction mappings which generalizes the concept of cyclic contraction mappings. We establish the existence of best proximity point of these mappings in the framework of $CAT_p(0)$…
In this paper, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for certain matrix operators on the Fibonacci difference sequence spaces l_{p}(F) and l_{infinite}(F) to be compact, where…
In this paper, we specify a set of optimal subspaces for $L_2$ approximation of three classes of functions in the Sobolev space $W^{(r)}_2$, defined on a segment and subject to certain boundary conditions. All of these subspaces are…
In this paper we continue the study of compact-like operators in lattice normed spaces started recently by Aydin, Emelyanov, Erkur\c{s}un \"Ozcand and Marabeh. We show among others, that every p-compact operator between lattice normed…
As continuation of the study of polynomial approximation and composition operators on Dirichlet spaces of unit disk, which has settled a problem posed by Cima in 1976, the present paper aims to consider the case of the unbounded domains,…
Extending and unifying concepts extensively used in the literature, we introduce the notion of approximable interpolation sets for algebras of functions on locally compact groups, especially for weakly almost periodic functions and for…
We establish new results on the $\mathcal I$-approximation property for the Banach operator ideal $\mathcal I=\mathcal{K}_{up}$ of the unconditionally $p$-compact operators in the case of $1\le p<2$. As a consequence of our results, we…
We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.
This paper is devoted to the study of the relatively compact sets in Quasi-Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness…
For the class of de Branges-Rovnyak spaces $\mathcal{H}(b)$ of the unit disk $\mathbb{D}$ defined by extreme points $b$ of the unit ball of $H^\infty$, we study the problem of approximation of a general function in $\mathcal{H}(b)$ by a…
We introduce and study the notion of reduced spectral synthesis, which unifies the concepts of spectral synthesis and uniqueness in locally compact groups. We exhibit a number of examples and prove that every non-discrete locally compact…
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
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…