6 papers
CPD th roots of subnormal operators are subnormal
Zenon Jan JabÅoÅski, Il Bong Jung, PaweÅ Pietrzycki +1
We investigate the th root problem for bounded operators on a Hilbert space within the class of conditionally positive definite (CPD) operators determined by the Lévy--Khintchi…
Hyperrigidity I: singly generated commutative -algebras
PaweÅ Pietrzycki, Jan Stochel
Although Arveson's hyperrigidity conjecture was recently resolved negatively by B. Bilich and A. Dor-On, the problem remains open for commutative -algebras. Relatively few exa…
Hyperrigidity II: -dilations, ideals and decompositions
PaweÅ Pietrzycki, Jan Stochel
We investigate the hyperrigidity of subsets of unital -algebras annihilated by states (or, more generally, by completely positive maps). This is closely related to the concept…
Cowen-Douglas operators and analytic continuation
PaweÅ Pietrzycki
In this paper, we study certain Banach spaces of analytic functions on which a left-invertible multiplication operator acts. It turns out that, under natural conditions, its left i…
A Shimorin-type analytic model on an annulus for left-invertible operators and applications
Pawel Pietrzycki
A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighte…
Hyperrigidity III
PaweÅ Pietrzycki, Paweł Pietrzycki, Jan Stochel +1
In this paper, we study hyperrigidity for -algebras. We will show that hyperrigidity can be expressed solely in terms of representations, without the need to involve general u…