In this paper we study the Foias-Williams operator T (Hg) = S∗ Hg 0 S where g ∈ L∞, and Hg is a Hankel operator with symbol g. We exhibit a relationship between the similarity of T (Hg) to a contraction and the rate of decay of {|gn|}n=0, the absolute values of the Fourier coefficients of the symbol g. Let H denote a complex Hilbert space and let L(H) denote the algebra of all bounded linear op...

Here we give a closure free description of the higher rank numerical range normal operator acting on separable Hilbert space. This generalizes result Avendaño for self-adjoint operators. It has several interesting applications. We show using Durszt's example that there exists contraction T which intersection ranges all unitary dilations contains as proper subset. strengthen and generalize Wu by...

We present a complete pretopology semantics for a system of Intuitionistic Linear Logic (commutative or not) where the storage operator is split into a contraction and a weakening component and then recovered again from them. The semantics for weakening and contraction has been explored by Bart Jacobs 13] in a categorical setting. However, a completeness theorem is not given in 13] and the appr...

A partial answer on [KS2, Question 2] is given. Namely, an operator $R$ similar to a quasianalytic contraction whose spectral set equal its spectrum and proper subarc of the unit circle constructed, but no estimates $\|R^{-1}\|$

Each relation induces a new closure operator, which is (in the sense of data mining) stronger than or equal to the Galois one. The goal is to give some evidence that the new closure operator is often properly stronger than the Galois one. An easy characterization of the new closure operator as a largest fixed point of an appropriate contraction map leads to a (modest) computer program. Finally,...

In this paper we construct a special sort of dilation for an arbitrary polynomially bounded operator. This enables us to show that the problem whether every polynomially bounded operator is similar to a contraction can be reduced to a subclass of it.

Two new approaches to the infinitesimal characterisation of quantum stochastic cocycles are reviewed. The first concerns mapping cocycles on an operator space and demonstrates the role of Hölder continuity; the second concerns contraction operator cocycles on a Hilbert space and shows how holomorphic assumptions yield cocycles enjoying an infinitesimal characterisation which goes beyond the sco...

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop notion $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points a new type contractive mappings complete metric spaces,} Fixed Point Theory Appl., 94, (2012)). To achieve this, introduce Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator also...