Related papers: Best approximation in spaces of compact operators

We demonstrate criteria, purely based on finite subwords of the potential, to guarantee spectral inclusion as well as Hausdorff approximation of pseudospectra or even spectra of generalized Schr\"odinger operators on the discrete line or…

We give a sufficient condition for a composition operator with positive characteristic to be compact on the Hardy space of Dirichlet series.

Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$…

We study a version of the functional Hodrick-Prescott filter where the associated operator is not necessarily compact, but merely closed and densely defined with closed range. We show that the associated optimal smoothing operator preserves…

In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…

A bounded linear operator $ A$ on a Hilbert space $ \mathcal H $ is said to be an $ EP $ (hypo-$ EP $) operator if ranges of $ A $ and $ A^* $ are equal (range of $ A $ is contained in range of $ A^* $) and $ A $ has a closed range. In this…

We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data…

We establish the weak Banach-Saks property for function spaces arising as the optimal domain of an operator.

In this note, we provide convergence results for the proximal point algorithm and a splitting variant thereof in the setting of CAT$(\kappa)$ spaces with $\kappa > 0$ using a recent definition for the resolvent of a convex, lower…

We study $M$-ideals of compact operators by means of the property~$(M)$ introduced in \cite{Kal-M}. Our main result states for a separable Banach space $X$ that the space of compact operators on $X$ is an $M$-ideal in the space of bounded…

We construct various examples of non-trivial closed ideals of the compact-by-approximable algebra $\mathfrak{A}_X =:\mathcal K(X)/\mathcal A(X)$ on Banach spaces $X$ failing the approximation property. The examples include the following:…

We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.

By a theorem of Bayart, $\varphi$ generates a bounded composition operator on the Hardy space $\Hp$of Dirichlet series ($1\le p<\infty$) only if $\varphi(s)=c_0 s+\psi(s)$, where $c_0$ is a nonnegative integer and $\psi$ a Dirichlet series…

In this paper, we study bounded and closed range multiplication and composition operators between two different Orlicz spaces.

We establish the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two weight setting on the spaces of homogeneous type in the sense of Coifman and Weiss. As a direct application…

We show that operators on a separable infinite dimensional Banach space $X$ of the form $I +S$, where $S$ is an operator with dense generalised kernel, must lie in the norm closure of the hypercyclic operators on $X$, in fact in the closure…

We determine the free field hypercubic Dirac operator which is optimally close to satisfying the Ginsparg-Wilson relation. Inserting this operator into the overlap formula, we show that the analytic locality bound on the resulting overlap…

In this paper we study, in the relaxed context of locally convex spaces, intrinsic properties of monotone operators needed for the sum conjecture for maximal monotone operators to hold under classical interiority-type domain constraints.

Let $\mathcal{H}_1,\ldots,\mathcal{H}_n,\mathcal{H}$ be complex Hilbert spaces and $A_k:\mathcal{H}_k\to\mathcal{H}$ be a bounded linear operator with the closed range $Ran(A_k)$, $k=1,\ldots,n$. It is known that if $A_i^*A_j$ is compact…

Let K be a (commutative) field, and U and V be finite-dimensional vector spaces over K. Let S be a linear subspace of the space L(U,V) of all linear operators from U to V. A map F from S to V is called range-compatible when F(s) belongs to…