• Honam Mathematical Journal
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• v.24 no.1
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• pp.9-23
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• 2002

For a closed densely defined linear operator T on a Hilbert space H, let ${\prod}$ denote the function which corresponds to T, the orthogonal projection from $H{\oplus}H$ onto the graph of T. We extend some ordinary norm ineqralites comparing ${\parallel}{\Pi}(A)-{\Pi}(B){\parallel}$ and ${\parallel}A-B{\parallel}$ to the Schatten p-norm where A and B are bounded operators on H.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.441-455
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• 2017

In this article we have determined the spectrum and fine spectrum of the lower triangular matrix B(r, s) on the Hahn sequence space h. We have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator B(r, s) on the sequence space h.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.235-249
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• 2024

We obtain a structured class of frames in separable Hilbert spaces which are generalizations of Gabor frames in L²(ℝ) in their construction aspects. For this, the concept of Gabor type unitary systems in [13] is generalized by considering a system of invertible operators in place of unitary systems. Pseudo Gabor like frames and pseudo Gabor frames are introduced and the corresponding frame operators are characterized.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.673-674
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• 2018

Corrections are made for some examples following Theorem 2.2 in Posinormal terraced matrices, Bull. Korean Math. Soc. 46 (2009), no. 1, 117-123.

• 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.

• 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.

• 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.

• 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 $\mathbb{C}^n$.

• 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.