• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.585-596
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• 2019

It is shown that a pair of Hilbert space operators V and W such that $V^*W=I$ (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal bases are replaced with biorthogonal sequences, and it is also shown how such a pair of biisometric operators yields a pair of biorthogonal sequences which are shifted by them. These are applied to a class of Laguerre operators on $L^2[0,{\infty})$.

• 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.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.363-382
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• 2014

In this paper we first characterize the hereditarily hypercyclicity of the unilateral (or bilateral) weighted shifts on the spaces $L^2(\mathbb{N},\mathcal{K})$ (or $L^2(\mathbb{Z},\mathcal{K})$) with weight sequence {$A_n$} of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$. Then we give the necessary and sufficient conditions for the supercyclicity of those weighted shifts, which extends some previous results of H. Salas. At last, we give some conditions for the supercyclicity of three different weighted shifts.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.579-590
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• 2020

The flatness property of a unilateral weighted shifts is important to study the gaps between subnormality and hyponormality. In this paper, we first summerize the results on the flatness for some special kinds of a weighted shifts. And then, we consider the flatness property for a local-cubically hyponormal weighted shifts, which was introduced in [2]. Let α : ${\sqrt{\frac{2}{3}}}$, ${\sqrt{\frac{2}{3}}}$, $\{{\sqrt{\frac{n+1}{n+2}}}\}^{\infty}_{n=2}$ and let W_α be the associated weighted shift. We prove that W_α is a local-cubically hyponormal weighted shift W_α of order ${\theta}={\frac{\pi}{4}}$ by numerical calculation.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.845-848
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• 2023

Erratum/Addendum to the paper "Biisometric operators and biorthogonal sequences" [Bull. Korean Math. Soc. 56 (2019), No. 3, pp. 585-596].

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.25-31
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• 2022

Let α = {α_n}^∞_n=0 be a weight sequence and let W_α denote the associated unilateral weighted shift on 𝑙²(Z₊). In this paper we will investigate which weighted shift is M-hyponormal.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.721-727
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• 2008

Let $W_{\alpha}$ be a weighted shift with positive weight sequence ${\alpha}=\{\alpha_i\}_{i=0}^{\infty}$. The semi-cubical hyponormality of $W_{\alpha}$ is introduced and some flatness properties of $W_{\alpha}$ are discussed in this note. In particular, it is proved that if ${\alpha}_n={\alpha}_{n+1}$ for some $n{\geq}1$, ${{\alpha}_{n+k}}={\alpha}_n$ for all $k{\geq}1$.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.225-251
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• 2018

The m-isometry of a single operator in Agler and Stankus [3] was naturally generalized to the m-isometric tuple of several commuting operators by Gleason and Richter [22]. Some examples of m-isometric tuples including the recently much studied Arveson-Drury d-shift were given in [22]. We provide more examples of m-isometric tuples of operators by using sums of operators or products of operators or functions of operators. A class of m-isometric tuples of unilateral weighted shifts parametrized by polynomials are also constructed. The examples in Gleason and Richter [22] are then obtained by choosing some specific polynomials. This work extends partially results obtained in several recent papers on the m-isometry of a single operator.

• The Journal of Korean Society for Radiation Therapy
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• v.34
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• pp.21-30
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• 2022

Purpose: The purpose of this study is to evaluate the effectiveness of oral positioning stent, the BinkieRT^TM in radiation treatment for head and neck cancer patients in terms of tongue positions reproducibility, tongue doses and material properties. Materials and Methods: 24 cases using BinkieRT^TM during radiation treatments were enrolled. The tongue was contoured on planning CT and CBCT images taken every 3 days during treatment, and then the DSC and center of tongue shift values were analyzed to evaluate the reproducibility of the tongue. The tongue dose was compared in terms of dose distribution when using BinkieRT^TM and different type of oral stents (mouthpiece, paraffin wax). Randomly selected respective 10 patients were measured tongue doses of initial treatment plan for nasal cavity and unilateral parotid cancer. Finally, In terms of material evaluation, HU and relative electron density were identified in RTPS. Results: As a result of DSC analysis, it was 0.8 ± 0.07, skewness -0.8, kurtosis 0.61, and 95% CI was 0.79~0.82. To analyze the deviation of the central tongue shift during the treatment period, a 95% confidence interval for shift in the LR, SI, and AP directions were indicated, and a one-sample t-test for 0, which is an ideal value in the deviation(n=144). As a result of the t-test, the mean and SD in the LR and SI directions were 0.01 ± 0.14 cm (p→.05), 0.03 ± 0.25 cm (p→.05), and -0.08 ± 0.25 cm (p ←.05) in the AP direction. In the case of unilateral parotid cancer patients, the Dmean to the tongue of patients using BinkieRT^TM was 16.92% ± 3.58% compared to the prescribed dose, and 23.99% ± 10.86% of patients with Paraffin Wax, indicating that the tongue dose was relatively lower when using BinkieRT^TM (p←.05). On the other hand, among nasal cavity cancer patients, the Dmean of tongue dose for patients who used BinkieRT^TM was 4.4% ± 5.6%, and for those who used mouthpiece, 5.9% ± 6.8%, but it was not statistically significant (p→.05). The relative electron density of Paraffin Wax, BinkieRT^TM and Putty is 0.94, 0.99, 1.26 and the mass density is 0.95, 0.99 and 1.32 (g/cc), Transmission Factor is 0.99, 0.98, 0.96 respectively. Conclusion: The result of the tongue DSC analysis over the treatment period was about 0.8 and Deviation of the center of tongue shifts were within 0.2 cm, the reproducibility was more likely excellent. In the case of unilateral head and neck cancer patients, it was found that the use of BinkieRT^TM rather than Paraffin Wax or Putty can reduce the unnecessary dose irradiated to the tongue. This study might be useful to understand of BinkieRT^TM's properties and advantages. And also it could be another considered option as oral stent to keep the reproducibility of tongue and reducing dose during head and neck radiation treatments.