http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Criteria for Algebraic Operators to be Unitary
Zenon Jan Jablonski,Jan Stochel,정일봉 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.1
Criteria for an algebraic operator T on a complex Hilbert space H to be unitary are established. The main one is written in terms of the convergence of sequences of the form {∥Tnh∥}∞n=0 with h ∈ H. Related questions are also discussed.
Generalized Friedland's theorem for C<sub>0</sub>-semigroups
Cichon, D.,Jung, I.B.,Stochel, J. Academic Press 2008 Journal of mathematical analysis and applications Vol.343 No.2
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C<SUB>0</SUB>-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
<i>L</i>(<i>n</i>)-HYPONORMALITY: A MISSING BRIDGE BETWEEN SUBNORMALITY AND PARANORMALITY
JUNG, IL BONG,PARK, SUN HYUN,STOCHEL, JAN Cambridge University Press 2010 JOURNAL- AUSTRALIAN MATHEMATICAL SOCIETY Vol.88 No.2
<B>Abstract</B><P>A new notion of <I>L</I>(<I>n</I>)-hyponormality is introduced in order to provide a bridge between subnormality and paranormality, two concepts which have received considerable attention from operator theorists since the 1950s. Criteria for <I>L</I>(<I>n</I>)-hyponormality are given. Relationships to other notions of hyponormality are discussed in the context of weighted shift and composition operators.</P>
On Normal Products of Selfadjoint Operators
Jung, Il Bong,Mortad, Mohammed Hichem,Stochel, Jan Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.3
A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator model for pairs (A, B) of selfadjoint operators such that B is bounded and AB is normal is established. The case when both operators A and B are bounded is discussed. In addition, the example due to Rehder is reexamined from this point of view.
Hyperexpansive completion problem via alternating sequences; an application to subnormality
Jabłoń,ski, Zenon J.,Jung, Il Bong,Kwak, Jung Ah,Stochel, Jan Elsevier 2011 Linear algebra and its applications Vol.434 No.12
<P><B>Abstract</B></P><P>Truncations of completely alternating sequences are entirely characterized. The completely hyperexpansive completion problem is solved for finite sequences of (positive) numbers in terms of positivity of attached matrices. Solutions to the problem are written explicitly for sequences of two, three, four, five and six numbers. As an application, an explicit solution of the subnormal completion problem for five numbers is given.</P>
Unbounded subnormal weighted shifts on directed trees. II
Budzynski, P.,Jablonski, Z.J.,Jung, I.B.,Stochel, J. Academic Press 2013 Journal of mathematical analysis and applications Vol.398 No.2
Criteria for subnormality of unbounded injective weighted shifts on leafless directed trees with one branching vertex are proposed. The case of classical weighted shifts is discussed. The relevance of an inductive limit approach to subnormality of weighted shifts on directed trees is revealed.
A multiplicative property characterizes quasinormal composition operators in L<sup>2</sup>-spaces
Budzynski, P.,Jablonski, Z.J.,Jung, I.B.,Stochel, J. Academic Press 2014 Journal of mathematical analysis and applications Vol.409 No.1
A densely defined composition operator in an L<SUP>2</SUP>-space induced by a measurable transformation φ is shown to be quasinormal if and only if the Radon-Nikodym derivatives h<SUB>φ^n</SUB> attached to powers φ<SUP>n</SUP> of φ have the multiplicative property: h<SUB>φ^n</SUB>=h<SUB>φ</SUB><SUP>n</SUP> almost everywhere for n=0,1,2,....
Subnormality of unbounded composition operators over one-circuit directed graphs: Exotic examples
Budzynski, P.,Jablonski, Z.J.,Jung, I.B.,Stochel, J. Academic Press ; Elsevier Science B.V. Amsterdam 2017 Advances in mathematics Vol.310 No.-
<P>A recent example of a non-hyponormal injective composition operator in an L-2-space generating Stieltjes moment sequences, invented by three of the present authors, was built over a non-locally finite directed tree. The main goal of this paper is to solve the problem of whether there exists such an operator over a locally finite directed graph and, in the affirmative case, to find the simplest possible graph with these properties (simplicity refers to local valency). The problem is solved affirmatively for the locally finite directed graph g(2,0), which consists of two branches and one loop. The only simpler directed graph for which the problem remains unsolved consists of one branch and one loop. The consistency condition, the only efficient tool for verifying subnormality of unbounded composition operators, is intensively studied in the context of g(2),(0), which leads to a constructive method of solving the problem. The method itself is partly based on transforming the Krein and the Friedrichs measures coming either from shifted Al-Salam-Carlitz q-polynomials or from a quartic birth and death process. (C) 2017 Elsevier Inc. All rights reserved.</P>