3 citations · 11 across the 14 of their papers we have counts for
14 papers
On the dimension of orbits of matrix pencils under strict equivalence
Fernando De Terán, Froilán M. Dopico, Patryk Pagacz
We prove that, given two matrix pencils and , if belongs to the closure of the orbit of under strict equivalence, then the dimension of the orbit of is smaller t…
The Taylor spectrum of pairs of isometries
Zbigniew Burdak, Patryk Pagacz
In the paper we fully describe Taylor spectrum of pairs of isometries given by diagrams. In most cases both isometries in such pairs have non-trivial shift part and its Taylor spec…
An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process
Zbigniew Burdak, Marek Kosiek, Patryk Pagacz +1
A new approach to the evanescent part of a two-dimensional weak-stationary stochastic process with the past given by a half-plane is proceed. The classical result due to Helson and…
On singular pencils with commuting coefficients
Vadym Koval, Patryk Pagacz
We investigate the relation between the spectrum of matrix (or operator) polynomials and the Taylor spectrum of its coefficients. We prove that the polynomial of commuting matrices…
On bundle closures of matrix pencils and matrix polynomials
Fernando De Terán, Froilán M. Dopico, Vadym Koval +1
Bundles of matrix polynomials are sets of matrix polynomials with the same size and grade and the same eigenstructure up to the specific values of the eigenvalues. It is known that…
Matrix pencils with the numerical range equal to the whole complex plane
Vadym Koval, Patryk Pagacz
The main purpose of this article is to show that the numerical range of a linear pencil is equal to if and only if belongs to the convex hull of the joint…
Target Layer Regularization for Continual Learning Using Cramer-Wold Generator
Marcin Mazur, Łukasz Pustelnik, Szymon Knop +2
We propose an effective regularization strategy (CW-TaLaR) for solving continual learning problems. It uses a penalizing term expressed by the Cramer-Wold distance between two prob…
The decomposition theorems in Baer -rings
Zbigniew Burdak, Marek Kosiek, Patryk Pagacz +1
We show a general decomposition theorem in Baer *-rings. As a consequence the vast majority of decompositions known in the algebra of bounded Hilbert space operators are generalize…
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…
Invariant subspaces of and preserving compatibility
Zbigniew Burdak, Marek Kosiek, Patryk Pagacz +1
Operators of multiplication by independent variables on the space of square summable functions over the torus and its Hardy subspace are considered. Invariant subspaces where the o…
Random Perturbations of Matrix Polynomials
Patryk Pagacz, Michał Wojtylak
A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial conve…
The Berberian's transform and an asymmetric Putnam-Fuglede theorem
Ahmed Bachir, Patryk Pagacz
We present how to apply a Berberian's technique to asymmetric Putnam-Fuglede theorems. In particular, we proved that if belong to the union of classes of -parano…
On the spectral properties of a class of -selfadjoint random matrices and the underlying combinatorics
Patryk Pagacz, Michal Wojtylak
An expansion of the Weyl function of a -selfadjoint random matrix with one negative square is provided. It is shown that the coefficients converge to a certain generalization of…
On the power-bounded operators of classes and
Patryk Pagacz
By a bounded backward sequence of the operator we mean a bounded sequence satisfying . In \cite{Pa} we have characterized contractions with strongly sta…