• 대한수학회보
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• 제46권3호
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• pp.447-461
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• 2009

In this paper we give a non-existence theorem for Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ satisfying the condition that the structure Jacobi operator $R_{\xi}$ commutes with the 3-structure tensors ${\phi}_i$, i = 1, 2, 3.

• 대한수학회논문집
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• 제10권1호
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• pp.57-65
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• 1995

Let R denote the set of real numbers, $R_+$ the non-negative real numbers and D and set of all distribution functions.(omitted)

• 대한수학회지
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• 제43권2호
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• pp.259-269
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• 2006

We obtain a characterization of commuting Toeplitz operators with holomorphic symbols acting on the pluriharmonic Bergman space of the polydisk. We also obtain a characterization of normal Toeplitz operators with pluriharmonic symbols. In addition, some results for special types of semi-commutators are included.

• 대한수학회보
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• 제51권1호
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• pp.207-211
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• 2014

The aim of this paper is to prove the next result. Let n > 1 be an integer and let R be a n!-torsion free semiprime ring. Suppose that f : R ${\rightarrow}$ R is an additive mapping satisfying the relation [f(x), $x^n$] = 0 for all $x{\in}R$. Then f is commuting on R.

• 대한수학회논문집
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• 제33권3호
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• pp.853-869
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• 2018

We give a new characterization of Browder's theorem through equality between the pseudo B-Weyl spectrum and the generalized Drazin spectrum. Also, we will give conditions under which pseudo B-Fredholm and pseudo B-Weyl spectrum introduced in [9] and [25] become stable under commuting Riesz perturbations.

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.221-226
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• 2007

In this note we set forth three possible definitions of the property of "almost commuting with a compact operator" and discuss an old result of W. Arveson that says that every operator on Hilbert space has the weakest of the three properties. Finally, we discuss some recent progress on the hyperinvariant subspace problem (see the bibliography), and relate it to the concept of almost commuting with a compact operator.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.271-278
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• 2007

Let R be a 2-torsion free semiprime ring. Suppose that there exists a 4-permuting 4-derivation ${\Delta}:R{\times}R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on R. Then the trace of ${\Delta}$ is commuting on R. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

• 충청수학회지
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• 제22권3호
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• pp.451-458
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• 2009

Let $n{\geq}2$ be a fixed positive integer and let R be a noncommutative n!-torsion free semiprime ring. Suppose that there exists a symmetric n-derivation $\Delta$ : $R^{n}{\rightarrow}R$ such that the trace of $\Delta$ is centralizing on R. Then the trace is commuting on R. If R is a n!-torsion free prime ring and $\Delta{\neq}0$ under the same condition. Then R is commutative.

• 대한수학회보
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• 제44권4호
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• pp.789-794
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• 2007

Let R be a 3-torsion free semiprime ring and let I be a nonzero two-sided ideal of R. Suppose that there exists a permuting 3-derivation ${\Delta}:R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on I. Then the trace of ${\Delta}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

• 대한수학회보
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• 제43권4호
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• pp.711-713
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• 2006

Let R be a semiprime ring and f be an endomorphism on R. If f is a strong commutativity preserving (simply, scp) map on a non-zero ideal U of R, then f is commuting on U.