• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.775-784
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• 1995

Let $H$ be a separable, infnite dimensional, complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.135-147
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• 1997

Let k be an infinite field and let $X = {P_1, \cdots, P_s}$ be a set of s-distinct points in $P^n$. We denote by $I(X)$ the defining ideal of $X$ in the polynomial ring $R = k[x_0, \cdots, x_n]$ and by A the homogeneous coordinate ring of $X, A = \sum_{t = 0}^{\infty} A_t$.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.635-647
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• 1995

Let $H$ denote a separable, infinite dimensional complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $1_H$ and is closed in the $weak^*$ operator topology on $L(H)$. For $T \in L(H)$, let $A_T$ denote the smallest subalgebra of $L(H)$ that contains T and $1_H$ and is closed in the $weak^*$ operator topology.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.875-882
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• 2004

Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{p}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.279-284
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• 1997

Let L/F be a finite separable extension of Henselian valued fields with same residue fields $\overline{L} = \overline{F}$. Let D be an inertially split division algebra over L, and let $^cD$ be the underlying division algebra of the corestriction $cor_{L/F} (D)$ of D. We show that the index $ind(^cD) of ^cD$ divides $[Z(\overline{D}) : Z(\overline {^cD})] \cdot ind(D), where Z(\overline{D})$ is the center of the residue division ring $\overline{D}$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.211-216
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• 2009

Let G be a Denjoy domain and let G' a Denjoy proper subdomain of G and homeomorphic to G. We consider conformal re-imbeddings of G' into G. Let G and G' are N-connected. We know that if N = 2, there is a re-imbedding f of G' into G such that G - cl(f(G')) has an interior point. In this note, we obtain the following theorem. If $N{\geq}3$, G has a Denjoy proper subdomain G' such that, for any re-imbeddings f of G' into G, G - cl(f(G') has no interior point.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.579-586
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• 2009

Let $\varphi$ be a complete probability measure on $\mathbb{R}$, let $m_{\varphi}$ be the analogue of Wiener measure over paths on [0, T] and let f(t) be continuously differentiable on [0, T]. In this note, we give the analogue of Wiener measure $m_{\varphi}$ of {x in C[0, T]$\mid$x(0) < f(0) and $x(s_0){\geq}f(s_{0})$ for some $s_{0}$ in [0, T]} by use of integral equation techniques. This result is a generalization of Park and Paranjape's 1974 result[1].

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.75-85
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• 1992

Let R be an associative ring and let G be a finite group of Jordan automorphisms of R. Let $R^G$ be the set of elements in R fixed by all $g{\in}G$. In this paper we will study the relationship between the Levitzki radical of $R^G$ and R as that a Jordan ring. We also show that if R is a P.I. algebra, then the algebraicity of $R^G$ implies the algebraicity of R.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.837-846
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• 1994

Let A denote a unital normed algebra over a field K = R or C and let e be the identity of A. Given $a \in A$ and $x \in A$ with $\Vert x \Vert = 1$, let $$ V(A, a, x) = {f(ax) : f \in A', f(x) = 1 = \Vert f \Vert}. $$ Then the (Bonsall and Duncan) numerical range of an element $a \in A$ is defined by $$ V(a) = \cup{V(A, a, x) : x \in A, \Vert x \Vert = 1}, $$ where A' denotes the dual of A. In [2], $V(a) = {f(a) : f \in A', f(e) = 1 = \Vert f \Vert}$.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.