Related papers: Operators near completely polynomially dominated o…

We investigate whether almost weak stability of an operator $T$ on a Banach space $X$ implies its almost weak polynomial stability. We show, using a modified version of the van der Corput Lemma that if $X$ is a Hilbert space and $T$ a…

Let $T$ be a bounded linear operator on a Hilbert space $H$ such that \[ \alpha[T^*,T]:=\sum_{n=0}^\infty \alpha_n T^{*n}T^n\ge 0. \] where $\alpha(t)=\sum_{n=0}^\infty \alpha_n t^n$ is a suitable analytic function in the unit disc…

Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…

We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…

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…

A question if a polynomially bounded operator is similar to a contraction was posed by Halmos and was answered in the negative by Pisier. His counterexample is an operator of infinite multiplicity, while all its restrictions on invariant…

Let $E,F$ be exact operators (For example subspaces of the $C^*$-algebra $K(H)$ of all the compact operators on an infinite dimensional Hilbert space $H$). We study a class of bounded linear maps $u\colon E\to F^*$ which we call tracially…

We prove several versions of Grothendieck's Theorem for completely bounded linear maps $T\colon E \to F^*$, when E and F are operator spaces. We prove that if E,F are $C^*$-algebras, of which at least one is exact, then every completely…

The question if polynomially bounded operator is similar to a contraction was posed by Halmos and was answered in the negative by Pisier. His counterexample is an operator of infinite multiplicity, while all its restrictions on invariant…

An operator $T$ on a Hilbert space $\mathcal H$ is called expansive, if $\|Tx\|\geq \|x\|$ ($x\in\mathcal H$). Expansive operators $T$ quasisimilar to the unilateral shift $S_N$ of finite multiplicity $N$ are studied. It is proved that…

We show that two operator algebras are strongly Morita equivalent (in the sense of Blecher, Muhly and Paulsen) if and only if their categories of operator modules are equivalent via completely contractive functors. Moreover, any such…

Let $T\colon H\to H$ be a bounded operator on Hilbert space. We say that $T$ has a polygonal type if there exists an open convex polygon $\Delta\subset {\mathbb D}$, with $\overline{\Delta}\cap{\mathbb T}\neq\emptyset$, such that the…

Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on…

We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix…

We shall say that a densely defined closed operator $T$ on a Hilbert space is balanced if $\cD(T)=\cD(T^*)$. Balanced operators are described in terms of their phase operators abnd their moduli. Examples of balanced operators are developed.…

This note deals with the operator $T^*T$, where $T$ is a densely defined operator on a complex Hilbert space. We reprove a recent result of Z. Sebesty\'en and Zs. Tarcsay [13]: If $T^*T$ and $TT^*$ are self-adjoint, then $T$ is closed. In…

A closed subspace of a Banach space $\cX$ is almost-invariant for a collection $\cS$ of bounded linear operators on $\cX$ if for each $T \in \cS$ there exists a finite-dimensional subspace $\cF_T$ of $\cX$ such that $T \cY \subseteq \cY +…

Let $\eps >0$. We prove that there exists an operator $T_\eps:\ell_2\to\ell_2$, such that for any polynomial $P$ we have $\|{P(T)}\| \leq(1+\eps)\|{P}\|_\infty$, but which is not similar to a contraction, {\it i.e.} there does not exist an…

Given a contraction A on a Hilbert space H, an operator T on H is said to be A-invariant if <Tx,x>=<TAx,Ax> for every x in H such that ||Ax||=||x||. In the special case in which both defect indices of A are equal to 1, we show that every…

A particular case of [07] was generalized from contractions to polynomially bounded operators in [G19]. Namely, it is proved in [G19] that if the unitary asymptote of a polynomially bounded operator $T$ contains the bilateral shift of…