• Title, Summary, Keyword: weighted shift operator

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HYPERCYCLIC OPERATOR WEIGHTED SHIFTS

  • Hazarika, Munmun;Arora, S.C.
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.4
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    • pp.589-598
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    • 2004
  • We consider bilateral operator weighted shift T on $L^2$(K) with weight sequence ${[A_{n}]_{n=-{\infty}}}^{\infty}$ of positive invertible diagonal operators on K. We give a characterization for T to be hypercyclic, and show that the conditions are far simplified in case T is invertible.

ON THE CYCLICTY OF ADJOINTS OF WEIGHTED SHIFTS

  • YOUSEFI, B.;TAGHAVI, M.
    • Honam Mathematical Journal
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    • v.26 no.2
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    • pp.147-153
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    • 2004
  • We provide some sufficient conditions for the adjoint of a unilateral weighted shift operator on a Hilbert space to be cyclic.

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ON THE UNICELLULARITY OF AN OPERATOR

  • Joo Ho Kang;Young Soo Jo
    • Communications of the Korean Mathematical Society
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    • v.10 no.4
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    • pp.907-916
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    • 1995
  • The unilateral weighted shift operator $W_r$ with the weighted sequence ${r^n}^\infty_{n=0}$ is unicellular if $0 < r < 1$. In general, A + B is not unicellular even if A and B are unicellular. We will prove that $W_r + W^2_r$ is unicellular if $0 < r < 1$.

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SUBNORMAL WEIGHTED SHIFTS WHOSE MOMENT MEASURES HAVE POSITIVE MASS AT THE ORIGIN

  • Lee, Mi Ryeong;Kim, Kyung Mi
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.16 no.4
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    • pp.217-223
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    • 2012
  • In this note we examine the effects on subnormality of adding a new weight or changing some weights for a given subnormal weighted shift. We consider a subnormal weighted shift with a positive point mass at the origin by means of continuous functions. Finally, we introduce some methods for evaluating point mass at the origin about moment measures associated with weighted shifts.

ON QUASI-A(n, κ) CLASS OPERATORS

  • Lee, Mi Ryeong;Yun, Hye Yeong
    • Communications of the Korean Mathematical Society
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    • v.28 no.4
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    • pp.741-750
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    • 2013
  • To study the operator inequalities, the notions of class A operators and quasi-class A operators are developed up to recently. In this paper, quasi-$A(n,{\kappa})$ class operator for $n{\geq}2$ and ${\kappa}{\geq}0$ is introduced as a new notion, which generalizes the quasi-class A operator. We obtain some structural properties of these operators. Also we characterize quasi-$A(n,{\kappa})$ classes for n and ${\kappa}$ via backward extension of weighted shift operators. Finally, we give a simple example of quasi-$A(n,{\kappa})$ operators with two variables.

WEIGHTED NORM ESTIMATE FOR THE GENERAL HAAR SHIFT OPERATORS VIA ITERATING BELLMAN FUNCTION METHOD

  • CHUNG, DAEWON
    • East Asian mathematical journal
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    • v.31 no.5
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    • pp.635-652
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    • 2015
  • It is shown that for a general Haar shift operator, and a weight in the $A_2$ weight class, we establish the weighted norm estimate which linearly depends on $A_2$-characteristic $[w]_{A_2}$. Although the result is now well known, we introduce the new method, which is called the iterated Bellman function method, to provide the estimate.

SOME INEQUALITIES OF WEIGHTED SHIFTS ASSOCIATED BY DIRECTED TREES WITH ONE BRANCHING POINT

  • KIM, BO GEON;SEO, MINJUNG
    • East Asian mathematical journal
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    • v.31 no.5
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    • pp.695-706
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    • 2015
  • Let ${\mathcal{H}}$ be an infinite dimensional complex Hilbert space, and let $B({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. Recall that an operator $T{\in}B({\mathcal{H})$ has property B(n) if ${\mid}T^n{\mid}{\geq}{\mid}T{\mid}^n$, $n{\geq}2$, which generalizes the class A-operator. We characterize the property B(n) of weighted shifts $S_{\lambda}$ over (${\eta},\;{\kappa}$)-type directed trees which appeared in the study of subnormality of weighted shifts over directed trees recently. In addition, we discuss the property B(n) of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with nonzero weights are being distinct with respect to $n{\geq}2$. And we give some properties of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with property B(2).

SYNDETIC SEQUENCES AND DYNAMICS OF OPERATORS

  • Rezaei, Hamid
    • Communications of the Korean Mathematical Society
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    • v.27 no.3
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    • pp.537-545
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    • 2012
  • In the present paper, we show that a continuous linear operator T on a Frechet space satisfies the Hypercyclic Criterion with respect to a syndetic sequence must satisfy the Kitai Criterion. On the other hand, an operator, hereditarily hypercyclic with respect to a syndetic sequence must be mixing. We also construct weighted shift operators satisfying the Hypercyclicity Criterion which do not satisfy the Kitai Criterion. In other words, hereditarily hypercyclic operators without being mixing.