• Title/Summary/Keyword: B-operator

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INEQUALITIES OF OPERATOR VALUED QUANTUM SKEW INFORMATION

  • Choi, Byoung Jin;Lee, Mi Ra
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.59-70
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    • 2021
  • In this paper, we study two operator-valued inequalities for quantum Wigner-Yanase-Dyson skew information related to module operators. These are extended results of the trace inequalities for Wigner-Yanase-Dyson skew information. Moreover, we study a sufficient condition to prove an uncertainty relation for operator-valued generalized quantum Wigner-Yanase-Dyson skew information related to module operators and a pair of functions (f, g). Also, we obtain several previous results of scalar-valued cases as a consequence of our main result.

MIXED RADIAL-ANGULAR INTEGRABILITIES FOR HARDY TYPE OPERATORS

  • Ronghui Liu ;Shuangping Tao
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.5
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    • pp.1409-1425
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    • 2023
  • In this paper, we are devoted to studying the mixed radial-angular integrabilities for Hardy type operators. As an application, the upper and lower bounds are obtained for the fractional Hardy operator. In addition, we also establish the sharp weak-type estimate for the fractional Hardy operator.

WEAK FACTORIZATIONS OF H1 (ℝn) IN TERMS OF MULTILINEAR FRACTIONAL INTEGRAL OPERATOR ON VARIABLE LEBESGUE SPACES

  • Zongguang Liu;Huan Zhao
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.6
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    • pp.1439-1451
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    • 2023
  • This paper provides a constructive proof of the weak factorizations of the classical Hardy space H1(ℝn) in terms of multilinear fractional integral operator on the variable Lebesgue spaces, which the result is new even in the linear case. As a direct application, we obtain a new proof of the characterization of BMO(ℝn) via the boundedness of commutators of the multilinear fractional integral operator on the variable Lebesgue spaces.

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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IDENTIFICATION OF HUMAN-INDUCED INITIATING EVENTS IN THE LOW POWER AND SHUTDOWN OPERATION USING THE COMMISSION ERROR SEARCH AND ASSESSMENT METHOD

  • KIM, YONGCHAN;KIM, JONGHYUN
    • Nuclear Engineering and Technology
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    • v.47 no.2
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    • pp.187-195
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    • 2015
  • Human-induced initiating events, also called Category B actions in human reliability analysis, are operator actions that may lead directly to initiating events. Most conventional probabilistic safety analyses typically assume that the frequency of initiating events also includes the probability of human-induced initiating events. However, some regulatory documents require Category B actions to be specifically analyzed and quantified in probabilistic safety analysis. An explicit modeling of Category B actions could also potentially lead to important insights into human performance in terms of safety. However, there is no standard procedure to identify Category B actions. This paper describes a systematic procedure to identify Category B actions for low power and shutdown conditions. The procedure includes several steps to determine operator actions that may lead to initiating events in the low power and shutdown stages. These steps are the selection of initiating events, the selection of systems or components, the screening of unlikely operating actions, and the quantification of initiating events. The procedure also provides the detailed instruction for each step, such as operator's action, information required, screening rules, and the outputs. Finally, the applicability of the suggested approach is also investigated by application to a plant example.

PROPERTIES OF OPERATOR MATRICES

  • An, Il Ju;Ko, Eungil;Lee, Ji Eun
    • Journal of the Korean Mathematical Society
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    • v.57 no.4
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    • pp.893-913
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    • 2020
  • Let 𝓢 be the collection of the operator matrices $\(\array{A&C\\Z&B}\)$ where the range of C is closed. In this paper, we study the properties of operator matrices in the class 𝓢. We first explore various local spectral relations, that is, the property (β), decomposable, and the property (C) between the operator matrices in the class 𝓢 and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class 𝓢, and as some applications, we provide the conditions for such operator matrices to satisfy a-Weyl's theorem and a-Browder's theorem, respectively.

POLYNOMIALLY DEMICOMPACT OPERATORS AND SPECTRAL THEORY FOR OPERATOR MATRICES INVOLVING DEMICOMPACTNESS CLASSES

  • Brahim, Fatma Ben;Jeribi, Aref;Krichen, Bilel
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.5
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    • pp.1351-1370
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    • 2018
  • In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.

ON BOUNDED OPERATOR Qq IN WEIGHT BLOCH SPACE

  • Choi, Ki Seong
    • Journal of the Chungcheong Mathematical Society
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    • v.13 no.1
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    • pp.131-138
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    • 2000
  • Let D be the open unit disk in the complex plane $\mathbb{C}$. For any q > 0, the operator $Q_q$ defined by $$Q_qf(z)=q\int_{D}\frac{f(\omega)}{(1-z{\bar{\omega}})^{1+q}}d{\omega},\;z{\in}D$$. maps $L^{\infty}(D)$ boundedly onto $B_q$ for each q > 0. In this paper, weighted Bloch spaces $\mathcal{B}_q$ (q > 0) are considered on the open unit ball in $\mathbb{C}^n$. In particular, we will investigate the possibility of extension of this operator to the Weighted Bloch spaces $\mathcal{B}_q$ in $\mathbb{C}^n$.

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SOME PROPERTIES OF INVARIANT SUBSPACES IN BANACH SPACES OF ANALYTIC FUNCTIONS

  • Hedayatian, K.;Robati, B. Khani
    • Honam Mathematical Journal
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    • v.29 no.4
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    • pp.523-533
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    • 2007
  • Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.