@article{MTMT:34950955,
	title = {JAN STOCHEL, A STELLAR MATHEMATICIAN},
	url = {https://m2.mtmt.hu/api/publication/34950955},
	author = {Chavan, Sameer and Curto, Raul and Jablonski, Zenon Jan and Jung, Il Bong and Putinar, Mihai},
	doi = {10.7494/OpMath.2024.44.3.303},
	journal-iso = {OPUSC MATHEMATICA},
	journal = {OPUSCULA MATHEMATICA},
	volume = {44},
	unique-id = {34950955},
	issn = {1232-9274},
	keywords = {MOMENT PROBLEM; Composition operator; unbounded subnormal operator; Cauchy dual},
	year = {2024},
	eissn = {2300-6919},
	pages = {303-321}
}

@article{MTMT:31492847,
	title = {Unitary equivalence of operator-valued multishifts},
	url = {https://m2.mtmt.hu/api/publication/31492847},
	author = {Gupta, Rajeev and Kumar, Surjit and Trivedi, Shailesh},
	doi = {10.1016/j.jmaa.2020.124032},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {487},
	unique-id = {31492847},
	issn = {0022-247X},
	abstract = {We systematically study various aspects of operator-valued multishifts. Beginning with basic properties, we show that the class of multishifts on the directed Cartesian product of rooted directed trees is contained in that of operator-valued multishifts. Further, we establish circularity, analyticity and wandering subspace property of these multishifts. In the rest part of the paper, we study the function theoretic behaviour of operator-valued multishifts. We determine the bounded point evaluation, reproducing kernel structure and the unitary equivalence of operator-valued multishifts with invertible operator weights. In contrast with a result of Lubin, it appears that the set of all bounded point evaluations of an operator-valued multishift may be properly contained in the joint point spectrum of the adjoint of underlying multishift. (C) 2020 Elsevier Inc. All rights reserved.},
	keywords = {circularity; Operator-valued multishift; Operator-valued reproducing kernel; Bounded point evaluation; Wandering subspace property},
	year = {2020},
	eissn = {1096-0813}
}

@article{MTMT:31730790,
	title = {Generalized Multipliers for Left-Invertible Operators and Applications},
	url = {https://m2.mtmt.hu/api/publication/31730790},
	author = {Pietrzycki, Pawel},
	doi = {10.1007/s00020-020-02598-1},
	journal-iso = {INTEGR EQUAT OPER TH},
	journal = {INTEGRAL EQUATIONS AND OPERATOR THEORY},
	volume = {92},
	unique-id = {31730790},
	issn = {0378-620X},
	abstract = {Generalized multipliers for a left-invertible operator T, whose formal Laurent series U-x(z) = Sigma(infinity)(n=1)(PETn x)1/z(n) + Sigma(infinity)(n=0) (PET/*n x)z(n), x is an element of H actually represent analytic functions on an annulus or a disc are investigated. We show that they are coefficients of analytic functions and characterize the commutant of some left-invertible operators, which satisfies certain conditions in its terms. In addition, we prove that the set of multiplication operators associated with a weighted shift on a rootless directed tree lies in the closure of polynomials in z and 1/z of the weighted shift in the topologies of strong and weak operator convergence.},
	keywords = {ANALYTIC MODEL; Composition operator; Commutant; Left-invertible operator; (Generalized) multipliers; Weighted shift on directed three},
	year = {2020},
	eissn = {1420-8989}
}

@article{MTMT:30989208,
	title = {A solution to the Cauchy dual subnormality problem for 2-isometries},
	url = {https://m2.mtmt.hu/api/publication/30989208},
	author = {Anand, Akash and Chavan, Sameer and Jablonski, Zenon Jan and Stochel, Jan},
	doi = {10.1016/j.jfa.2019.108292},
	journal-iso = {J FUNCT ANAL},
	journal = {JOURNAL OF FUNCTIONAL ANALYSIS},
	volume = {277},
	unique-id = {30989208},
	issn = {0022-1236},
	abstract = {The Cauchy dual subnormality problem asks whether the Cauchy dual operator T' := T(T*T)(-1) of a 2-isometry T is subnormal. In the present paper we show that the problem has a negative solution. The first counterexample depends heavily on a reconstruction theorem stating that if T is a 2-isometric weighted shift on a rooted directed tree with nonzero weights that satisfies the perturbed kernel condition, then T' is subnormal if and only if T satisfies the (unperturbed) kernel condition. The second counterexample arises from a 2-isometric adjacency operator of a locally finite rooted directed tree again by thorough investigations of positive solutions of the Cauchy dual subnormality problem in this context. We prove that if T is a 2-isometry satisfying the kernel condition or a quasi-Brownian isometry, then T' is subnormal. We construct a 2-isometric adjacency operator T of a rooted directed tree such that T does not satisfy the kernel condition, T is not a quasi-Brownian isometry and T' is subnormal. (C) 2019 Elsevier Inc. All rights reserved.},
	keywords = {Cauchy dual operator; 2-isometry; Subnormal operator; Weighted shift on a directed tree},
	year = {2019},
	eissn = {1096-0783}
}

@article{MTMT:30546604,
	title = {Weighted shifts on directed trees: their multiplier algebras, reflexivity and decompositions},
	url = {https://m2.mtmt.hu/api/publication/30546604},
	author = {Budzynski, P. and Dymek, P. and Planeta, A. and Ptak, M.},
	doi = {10.4064/sm170220-20-9},
	journal-iso = {STUD MATH},
	journal = {STUDIA MATHEMATICA},
	volume = {244},
	unique-id = {30546604},
	issn = {0039-3223},
	abstract = {We study bounded weighted shifts on directed trees. We show that the set of multiplication operators associated with an injective weighted shift on a rooted directed tree coincides with the WOT/SOT closure of the set of polynomials of the weighted shift. From this fact we deduce reflexivity of those weighted shifts on rooted directed trees whose all path-induced spectral-like radii are positive. We show that weighted shifts with positive weights on rooted directed trees admit a Wold-type decomposition. We prove that the pairwise orthogonality of the factors in the decomposition is equivalent to the weighted shift being balanced.},
	keywords = {weighted shift on directed tree; multiplication operator; reflexive algebras; Wold-type decomposition},
	year = {2019},
	eissn = {1730-6337},
	pages = {285-308}
}

@article{MTMT:30989209,
	title = {A Shimorin-type analytic model on an annulus for left-invertible operators and applications},
	url = {https://m2.mtmt.hu/api/publication/30989209},
	author = {Pietrzycki, Pawel},
	doi = {10.1016/j.jmaa.2019.04.027},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {477},
	unique-id = {30989209},
	issn = {0022-247X},
	abstract = {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 weighted shift is introduced and investigated. We show that a left-invertible operator T, which satisfies certain conditions can be modeled as a multiplication operator M-z on a reproducing kernel Hilbert space of vector-valued analytic functions on an annulus or a disc. A similar result for composition operators in l(2)-spaces is established. (C) 2019 Elsevier Inc. All rights reserved.},
	keywords = {ANALYTIC MODEL; Weighted composition operator; Reproducing kernel Hilbert space; weighted shift on directed tree; multiplication operator; Hilbert space of holomorphic functions},
	year = {2019},
	eissn = {1096-0813},
	pages = {885-911},
	orcid-numbers = {Pietrzycki, Pawel/0000-0002-1830-7436}
}

@{MTMT:30546605,
	title = {Unbounded Weighted Composition Operators in L-2-Spaces Preface},
	url = {https://m2.mtmt.hu/api/publication/30546605},
	author = {Budzynski, Piotr and Jablonski, Zenon and Jung, Il Bong and Stochel, Jan},
	booktitle = {UNBOUNDED WEIGHTED COMPOSITION OPERATORS IN L2-SPACES},
	unique-id = {30546605},
	year = {2018},
	pages = {VII-+}
}

@article{MTMT:30464593,
	title = {Reduced commutativity of moduli of operators},
	url = {https://m2.mtmt.hu/api/publication/30464593},
	author = {Pietrzycki, Pawel},
	doi = {10.1016/j.laa.2018.08.007},
	journal-iso = {LINEAR ALGEBRA APPL},
	journal = {LINEAR ALGEBRA AND ITS APPLICATIONS},
	volume = {557},
	unique-id = {30464593},
	issn = {0024-3795},
	abstract = {In this paper, we investigate the question of when the equations A*(s)A(s) = (A*A)(s), s is an element of S, where S is a finite set of positive integers, imply the quasinormality or normality of A. In particular, it is proved that if S = {p, m, m + p, n, n +p}, where p >= 1 and 2 <= m < n, then A is quasinormal. Moreover, if A is invertible and S = {m, n, n+m} with m <= n, then A is normal. The case when S = {m, m+n} and A*(n)A(n) <= (A*A)(n) is also discussed. (C) 2018 Elsevier Inc. All rights reserved.},
	keywords = {Operator convex function; Normal operator; Quasinormal operator; Davis-Choi-Jensen inequality; Operator equation; Operator inequality; Weighted shift},
	year = {2018},
	eissn = {1873-1856},
	pages = {375-402}
}