Related papers: On the denseness of minimum attaining operators

The purpose of this note is to show that, if $\mcB$ is a uniformly convex Banach, then the dual space $\mcB'$ has a "Hilbert space representation" (defined in the paper), that makes $\mcB$ much closer to a Hilbert space then previously…

This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…

We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \quad z \in \ol \Sigma = \{z\in\bbC\,|\, \Re(z) \in [0,1]\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$.…

Let H be a separable Hilbert space with a fixed orthonormal basis (e_n), n>=1, and B(H) be the full von Neumann algebra of the bounded linear operators T: H -> H. Identifying l^\infty = C(\beta N) with the diagonal operators, we consider…

We construct a weak Hilbert Banach space such that for every block subspace $Y$ every bounded linear operator on Y is of the form D+S where S is a strictly singular operator and D is a diagonal operator. We show that this yields a weak…

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…

In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space $\mathcal{H}$, which are bounded with respect to the seminorm induced by a positive operator $A$ on…

We show that an infinite Toeplitz+Hankel matrix $T(\varphi) + H(\psi)$ generates a bounded (compact) operator on $\ell^p(\mathbb{N}_0)$ with $1\leq p\leq \infty$ if and only if both $T(\varphi)$ and $H(\psi)$ are bounded (compact). We also…

Let $B(H)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space $H$. For $T \in B(H)$ and $\lambda \in \mathbb{C}$, let $H_{T}(\{\lambda\})$ denotes the local spectral subspace of $T$ associated…

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…

The paper is concerned with the following question: if $A$ and $B$ are two bounded operators between Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$, and $\mathcal{M}$ and $\mathcal{N}$ are two closed subspaces in $\mathcal{H}$, when will…

Let $A$ be a positive bounded linear operator on a complex Hilbert space $\mathcal{H}$ and $\mathcal{B}_{A}(\mathcal{H})$ be the subspace of all operators which admit $A$-adjoints operators. In this paper, we establish some inequalities…

This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of…

We study the existence and characterization properties of compact Hermitian operators C on a separable Hilbert space H such that ||C|| is less or equal than || C + D ||, for all D in D(K(H)). This property is equivalent to || C || =…

Assume that $A$ is a closed linear operator defined on all of a Hilbert space $H$. Then $A$ is bounded. A new short proof of this classical theorem is given on the basis of the uniform boundedness principle. The proof can be easily extended…

A bounded linear operator $A$ on a Hilbert space $\mathcal{H}$ is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. We show that if $A$ is posinormal with closed range, then $A^n$ is posinormal and has closed…

Let $\lambda$ be a complex number in the closed unit disc $\overline{\Bbb D}$, and $\cal H$ be a separable Hilbert space with the orthonormal basis, say, ${\cal E}=\{e_n:n=0,1,2,\cdots\}$. A bounded operator $T$ on $\cal H$ is called a {\em…

Given Hilbert space operators $P,T\in B(\H), P\geq 0$ invertible, $T$ is $(m,P)-$ expansive (resp., $(m,P)-$ isometric) for some positive integer $m$ if…

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…

It is shown that if $1<p<\infty$ and $X$ is a subspace or a quotient of an $\ell_p$-direct sum of finite dimensional Banach spaces, then for any compact operator $T$ on $X$ such that $\|I+T\|>1$, the operator $I+T$ attains its norm. A…