16 citations · 58 across the 14 of their papers we have counts for
15 papers
Reduced Embry characterizations of quasinormal operators
Paweł Pietrzycki
We prove that, for any two integers , a bounded operator on a complex Hilbert space satisfying \[ A^{*k}A^k=(A^*A)^k, \qquad k\in\{m,n\}, \] is quasinormal. More gene…
CPD th roots of subnormal operators are subnormal
Zenon Jan Jabłoński, Il Bong Jung, Paweł 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--Khintchin…
Cowen-Douglas operators and analytic continuation
Paweł 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…
Hyperrigidity III
Paweł Pietrzycki, Marcel Scherer, Jan Stochel
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…
Hyperrigidity II: -dilations, ideals and decompositions
Paweł 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…
Hyperrigidity I: singly generated commutative -algebras
Paweł 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…
Two-moment characterization of spectral measures on the real line
Paweł Pietrzycki, Jan Stochel
Kiukas, Lahti and Ylinen asked the following general question. When is a positive operator measure projection valued? A version of this question formulated in terms of operator mom…
On th roots of bounded and unbounded quasinormal operators
Paweł Pietrzycki, Jan Stochel
In a recent paper [9], R. E. Curto, S. H. Lee and J. Yoon asked the following question: Let be a subnormal operator, and assume that is quasinormal. Does it follow that $…
Subnormal th roots of quasinormal operators are quasinormal
Paweł Pietrzycki, Jan Stochel
In the recent paper, R. E. Curto, S. H. Lee, J. Yoon, asked the following question: Let be a subnormal operator, and assume that is quasinormal. Does it follow that i…
On Cauchy dual operator and duality for Banach spaces of analytic functions
Paweł Pietrzycki
In this paper, two related types of dualities are investigated. The first is the duality between left-invertible operators and the second is the duality between Banach spaces of ve…
Between the von Neumann inequality and the Crouzeix conjecture
Patryk Pagacz, Paweł Pietrzycki, Michał Wojtylak
A new concept of a deformed numerical range is introduced. Here is a bounded linear operator or a matrix and is a parameter. Each is a clos…
Generalized multipliers for left-invertible operators and applications
Pawel Pietrzycki
We introduce generalized multipliers for left-invertible operators which formal Laurent series $U_x(z)=\sum_{n=1}^\infty(P_ET^{n}x) \frac{1}{z^n}+\sum_{n=0}^\infty(P_E{T^{\prime*}}…
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…
Reduced commutativity of moduli of operators
Paweł Pietrzycki
In this paper, we investigate the question of when the equations for all , where is a finite set of positive integers, imply the quasinormal…
The single equality does not imply the quasinormality of weighted shifts on rootless directed trees
Paweł Pietrzycki
It is proved that each bounded injective bilateral weighted shift satisfying the equality for some integer is quasinormal. For any integer…