• 충청수학회지
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• 제28권2호
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• pp.261-267
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• 2015

We study backward extensions of 2-variable weighted shifts with finite atomic Berger measure. We provide a necessary and sufficient condition for the subnormality of such extensions. As an application, we give a simple counterexample for the Curto-Muhly-Xia conjecture [10].

• 호남수학학술지
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• 제39권1호
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• pp.83-91
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• 2017

In this note we consider weakly hyponormal weighted shift. In particular, we focus on the weak 4-hyponormality of the weighted shift with the Bergman tail. This is related to the open question of finding a polynomially hyponormal non-subnormal weighted shift.

• 충청수학회지
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• 제26권1호
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• pp.181-190
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• 2013

In this paper we study the Putinar's matricial model operator of rank 2 and provide some evidences for the validity of the conjecture in [8].

• 대한수학회지
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• 제44권4호
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• pp.855-861
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• 2007

Let A and B be commuting bounded linear operators on a Hilbert space. In this paper, we study spectral area estimates for norms of $A^*B-BA^*$ when A is subnormal or p-hyponormal.

• Kyungpook Mathematical Journal
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• 제48권2호
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• pp.281-286
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• 2008

In this note we prove that if A and $B^*$ are subnormal operators and is a bounded linear operator such that AX - XB is a Hilbert-Schmidt operator, then f(A)X - Xf(B) is also a Hilbert-Schmidt operator and $${\parallel}f(A)X\;-\;Xf(B){\parallel}_2\;\leq\;L{\parallel}AX\;-\;XB{\parallel}_2$$, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and $X\;{\in}\;\cal{L}(\cal{H})$ is such that SX - XT belongs to a norm ideal (J, ${\parallel}\;{\cdot}\;{\parallel}_J$) and prove that f(S)X - Xf(T) $\in$ J and ${\parallel}f(S)X\;-\;Xf(T){\parallel}_J\;\leq\;C{\parallel}SX\;-\;XT{\parallel}_J$, for f in a certain class of functions.

• 대한수학회보
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• 제30권1호
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• pp.65-70
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• 1993

In this paper we will extend some notions of bounded linear operators to some unbounded linear operators. Let H be a complex separable Hilbert space and let B(H) denote the algebra of bounded linear operators. A closed densely defind linear operator S in H, with domain domS, is called subnormal if there is a Hilbert space K containing H and a normal operator N in K(i.e., $N^{*}$N=N $N^*/)such that domS .subeq. domN and Sf=Nf for f .mem. domS. we will show that the Radjavi and Rosenthal theorem holds for some unbounded subnormal operators; if $S_{1}$ and $S_{2}$ are unbounded subnormal operators on H with dom $S_{1}$= dom $S^{*}$$_{1}$ and dom $S_{2}$=dom $S^{*}$$_{2}$ and A .mem. B(H) is injective, has dense range and $S_{1}$A .coneq. A $S^{*}$$_{2}$, then $S_{1}$ and $S_{2}$ are normal and $S_{1}$.iden. $S^{*}$$_{2}$.2}$.X>.

• 대한수학회보
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• 제52권4호
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• pp.1353-1363
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• 2015

Let D be a division ring and w($x_1,\;x_2,\;{\ldots},\;x_m$) be a generalized group monomial over $D^*$. In this paper, we investigate subnormal subgroups and maximal subgroups of $D^*$ which satisfy the identity $w(x_1,\;x_2,\;{\ldots},\;x_m)=1$.

• 대한수학회보
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• 제46권4호
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• pp.607-615
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• 2009

In this paper, we investigate the growth of solutions and the existence of subnormal solutions for a class of higher order linear differential equations. We obtain some results which improve and extend the results of Chen-Shon [2] and Gundersen-Steinbart [5].

• East Asian mathematical journal
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• 제28권3호
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• pp.333-337
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• 2012

Finiteness of regular normal binary Hermitian lattices are known in several articles. In this article, we point out that there are infinitely many imaginary quadratic fields that admit a regular subnormal binary Hermitian lattice.

• 대한수학회논문집
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• 제34권2호
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• pp.477-486
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• 2019

Let ${\alpha}:1,(1,{\sqrt{x}},{\sqrt{y}})^{\wedge}$ be a weight sequence with Stampfli's subnormal completion and let $W_{\alpha}$ be its associated weighted shift. In this paper we discuss some properties of the region ${\mathcal{U}}:=\{(x,y):W_{\alpha}$ is semi-cubically hyponormal} and describe the shape of the boundary of ${\mathcal{U}}$. In particular, we improve the results of [19, Theorem 4.2].