• 대한수학회논문집
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• 제18권4호
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• pp.695-701
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• 2003

In this paper, we have characterizations of almost P-spaces which are analogous characterizations of P-spaces and we will show that if X is an almost P-space such that it is $C^{*}-embedded$ in every almost P-space in which X is embedded, then $$\mid${\upsilon}X-X$\mid${\leq}1$ and that if $$\mid${\upsilon}X-X$\mid${\leq}1$ and ${\upsilon}X$ is Lindelof, then for any almost P-space Y in which X is dense embedded, then X is $C^{*}-embeded$ in Y.

• Communications for Statistical Applications and Methods
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• 제21권4호
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• pp.317-325
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• 2014

Consider a nonlinear transform ${\Phi}(x)$ of x in $\mathbb{R}^p$ to Hilbert space H and assume that the dot product between ${\Phi}(x)$ and ${\Phi}(x^{\prime})$ in H is given by < ${\Phi}(x)$, ${\Phi}(x^{\prime})$ >= K(x, x'). The aim of this paper is to propose a mathematical technique to take screen shots of the multivariate dataset mapped to Hilbert space H, particularly suited to Gaussian kernel $K({\cdot},{\cdot})$, which is defined by $K(x,x^{\prime})={\exp}(-{\sigma}{\parallel}x-x^{\prime}{\parallel}^2)$, ${\sigma}$ > 0. Several numerical examples are given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권2호
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• pp.151-159
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• 1997

Observing that for any dense weakly Lindelof subspace of a space Y, X is $Z^{#}$ -embedded in Y, we show that for any weakly Lindelof space X, the minimal Cloz-cover ($E_{cc}$(X), $z_{X}$) of X is given by $E_{cc}$(X) = {(\alpha, \chi$) : $\alpha$ is a G(X)-ultrafilter on X with $\chi\in\cap\alpha$}, $z_{X}$=(($\alpha, \chi$))=$\chi$, $z_{X}$ is $Z^{#}$ -irreducible and $E_{cc}$(X) is a dense subspace of $E_{cc}$($\beta$X).

• 충청수학회지
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• 제4권1호
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• pp.103-113
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• 1991

Some properties of a path space and the fundamental group ${\sigma}(X,x_0,G)$ of a topological transformation group (X, G, ${\pi}$) are described. It is shown that ${\sigma}(X,x_0,H)$ is a normal subgroup of ${\sigma}(X,x_0,G)$ if H is a normal subgroup of G ; Let (X, G, ${\pi}$) be a transformation group with the open action property. If every identification map $p:{\Sigma}(X,x,G)\;{\longrightarrow}\;{\sigma}(X,x,G)$ is open for each $x{\in}X$, then ${\lambda}$ induces a homeomorphism between the fundamental groups ${\sigma}(X,x_0,G)$ and ${\sigma}(X,y_0,G)$ where ${\lambda}$ is a path from $x_0$ to $y_0$ in X ; The space ${\sigma}(X,x_0,G)$ is an H-space if the identification map $p:{\Sigma}(X,x_0,G)\;{\longrightarrow}\;{\sigma}(X,x_0,G)$ is open in a topological transformation group (X, G, ${\pi}$).

• 대한수학회논문집
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• 제38권2호
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• pp.643-648
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• 2023

Let X be a simply connected rationally elliptic space such that H²(X; ℚ) ≠ 0. In this paper, we show that if H²ⁿ(X^[2n-2]; ℚ) = 0 or if π_2n(X²ⁿ) ⊗ ℚ = 0 for all n, then X is an F₀-space.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.517-523
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• 1998

In this paper we prove that a normed almost linear space \hat{X} can be embedded in a normed linear space X when a normed almost linear space X has a basis and splits as X=V+W. Also we have a metric induced by a norm on a normed almost linear space as a corollary.

• 충청수학회지
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• 제22권4호
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• pp.831-841
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• 2009

For a map f : A $\rightarrow$ X, we define and study a concept of $G^f$-space for a map, which is a generalized one of a G-space. Any G-space is a $G^f$-space, but the converse does not hold. In fact, $S^2$ is a $G^{\eta}$-space, but not G-space. We show that X is a $G^f$-space if and only if $G_n$(A, f,X) = $\pi_n(X)$ for all n. It is clear that any $H^f$-space is a $G^f$-space and any $G^f$-space is a $W^f$-space. We can also obtain some results about $G^f$-spaces in Postnikov systems for spaces, which are generalization of Haslam's results about G-spaces.

• 대한수학회논문집
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• 제10권4호
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• pp.855-866
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• 1995

We prove that if a nals X is reflexive, then $X = W_X + V_X$. We prove also that if an als X has a finite basis, then $X = W_X + V_X$ if and only if X is reflexive.

• Korean Journal of Mathematics
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• 제15권1호
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• pp.13-26
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• 2007

We prove that every strong null sequence in a Banach space X lies inside the range of a vector measure of bounded variation if and only if the condition $\mathcal{N}_1(X,{\ell}_1)={\Pi}_1(X,{\ell}_1)$ holds. We also prove that for $1{\leq}p&lt;{\infty}$ every strong ${\ell}_p$ sequence in a Banach space X lies inside the range of an X-valued measure of bounded variation if and only if the identity operator of the dual Banach space $X^*$ is ($p^{\prime}$,1)-summing, where $p^{\prime}$ is the conjugate exponent of $p$. Finally we prove that a Banach space X has the property that any sequence lying in the range of an X-valued measure actually lies in the range of a vector measure of bounded variation if and only if the condition ${\Pi}_1(X,{\ell}_1)={\Pi}_2(X,{\ell}_1)$ holds.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.1-6
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• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.