• 대한수학회논문집
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• 제35권1호
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• pp.151-159
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• 2020

We introduce the notion of (m, n)-paranormal operators and (m, n)^⁎-paranormal operators on Hilbert space and study their properties. We also characterize these operators. Examples of operators are given which are (m, n)-paranormal but not (m, n)^⁎-paranormal, and vice-versa.

• 대한수학회지
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• 제44권1호
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• pp.25-34
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• 2007

An operator $T{\in}L(H)$ is said to be p-paranormal if $$\parallel{\mid}T\mid^pU{\mid}T\mid^px{\parallel}x\parallel\geq\parallel{\mid}T\mid^px\parallel^2$$ for all $x{\in}H$ and p > 0, where $T=U{\mid}T\mid$ is the polar decomposition of T. It is easy that every 1-paranormal operator is paranormal, and every p-paranormal operator is paranormal for 0 < p < 1. In this note, we discuss some properties for p-paranormal operators.

• 대한수학회논문집
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• 제38권4호
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• pp.1075-1090
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• 2023

In this paper, we study new classes of operators k-quasi (m, n)-paranormal operator, k-quasi (m, n)^*-paranormal operator, k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operator which are the generalization of (m, n)-paranormal and (m, n)^*-paranormal operators. We give matrix characterizations for k-quasi (m, n)-paranormal and k-quasi (m, n)^*-paranormal operators. Also we study some properties of k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operators. Moreover, these classes of composition operators on L² spaces are characterized.

• 충청수학회지
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• 제25권4호
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• pp.655-668
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• 2012

An operator $T\;{\varepsilon}\;B(\mathcal{H})$ is said to be $k$-quasi-paranormal operator if $||T^{k+1}x||^2\;{\leq}\;||T^{k+2}x||\;||T^kx||$ for every $x\;{\epsilon}\;\mathcal{H}$, $k$ is a natural number. This class of operators contains the class of paranormal operators and the class of quasi - class A operators. In this paper, using the operator matrix representation of $k$-quasi-paranormal operators which is related to the paranormal operators, we show that every algebraically $k$-quasi-paranormal operator has Bishop's property ($\beta$), which is an extension of the result proved for paranormal operators in [32]. Also we prove that (i) generalized Weyl's theorem holds for $f(T)$ for every $f\;{\epsilon}\;H({\sigma}(T))$; (ii) generalized a - Browder's theorem holds for $f(S)$ for every $S\;{\prec}\;T$ and $f\;{\epsilon}\;H({\sigma}(S))$; (iii) the spectral mapping theorem holds for the B - Weyl spectrum of T.

• Asian Journal for Public Opinion Research
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• 제2권4호
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• pp.279-306
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• 2015

Americans continue to have beliefs in the paranormal, for example in UFOs, ghosts, haunted houses, and clairvoyance. Yet, to date there has not been a systematic gathering of data on popular beliefs about the paranormal, and the question of whether or not there is a convincing trend in beliefs about the paranormal remains to be explored. Public opinion polling on paranormal beliefs shows that these beliefs have remained stable over time, and in some cases have in fact increased. Beliefs in ghosts (25% in 1990 to 32% in 2005) and haunted houses (29% in 1990, 37% in 2001) have all increased while beliefs in clairvoyance (26% in 1990 and 2005) and astrology as scientific (31% in 2006, 32% in 2014) have remained stable. Belief in UFOs (50%) is highest among all paranormal beliefs. Our findings show that people continue to hold beliefs about the paranormal despite their lack of grounding in science or religion.

• 대한수학회논문집
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• 제31권3호
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• pp.549-565
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• 2016

A Hilbert space operator $T{\in}{\mathfrak{B}}(\mathfrak{H})$ is said to be n-*-paranormal, $T{\in}C(n)$ for short, if ${\parallel}T^*x{\parallel}^n{\leq}{\parallel}T^nx{\parallel}\;{\parallel}x{\parallel}^{n-1}$ for all $x{\in}{\mathfrak{H}}$. We proved some properties of class C(n) and we proved an asymmetric Putnam-Fuglede theorem for n-*-paranormal. Also, we study some invariants of Weyl type theorems. Moreover, we will prove that a class n-* paranormal operator is finite and it remains invariant under compact perturbation and some orthogonality results will be given.

• Korean Journal of Mathematics
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• 제23권2호
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• pp.249-257
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• 2015

For a positive integer k, an operator T is said to be k-quasi-*-paranormal if ${\parallel}T^{k+2}x{\parallel}{\parallel}T^kx{\parallel}{\geq}{\parallel}T^*T^kx{\parallel}^2$ for all x $\in$ H, which is a generalization of *-paranormal operator. In this paper, we give a necessary and sufficient condition for T to be a k-quasi-*-paranormal operator. We also prove that the spectrum is continuous on the class of all k-quasi-*-paranormal operators.

• 대한수학회논문집
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• 제27권3호
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• pp.565-570
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• 2012

In this note we investigate Weyl's theorem for *-paranormal operators on a separable infinite dimensional Hilbert space. We prove that if T is a *-paranormal operator satisfying Property $(E)-(T-{\lambda}I)H_T(\{{\lambda}\})$ is closed for each ${\lambda}{\in}{\mathbb{C}}$, where $H_T(\{{\lambda}\})$ is a local spectral subspace of T, then Weyl's theorem holds for T.

• 호남수학학술지
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• 제26권2호
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• pp.137-145
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• 2004

we shall study some properties of a new class ($\sqrt[\kappa]{P}$) (defined below). Also we show that T may not be normaloid when $T{\in}(\sqrt[\kappa]{P})$, and that the class ($\sqrt{H}$) may not have the translation-invariant propety.

• 대한수학회보
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• 제39권4호
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• pp.571-575
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• 2002

In this paper we show that Weyl's theorem holds for f(T) when an Hilbert space operator T is “algebraically totally-paranormal” and f is any analytic function on an open neighbor-hood of the spectrum of T.