• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.427-433
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• 2013

Observing that every Tychonoff space X has an extension $kX$ which is a weakly Lindel$\ddot{o}$f space and the minimal quasi-F cover $QF(kX)$ of $kX$ is a weakly Lindel$\ddot{o}$f, we show that ${\Phi}_{kX}:QF(kX){\rightarrow}kX$ is a $z^{\sharp}$-irreducible map and that $QF({\beta}X)=QF(kX)$. Using these, we prove that $QF(kX)=kQF(X)$ if and only if ${\Phi}^k_X:kQF(X){\rightarrow}kX$ is an onto map and ${\beta}QF(X)=(QF{\beta}X)$.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.93-104
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• 2021

In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadžić type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.97-103
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• 2009

Suppose F is a field of characteristic not 2 and $F\;{\neq}\;Z_3$. Let $M_n(F)$ be the linear space of all $n{\times}n$ matrices over F, and let ${\Gamma}_n(F)$ be the subset of $M_n(F)$ consisting of all $n{\times}n$ involutory matrices. We denote by ${\Phi}_n(F)$ the set of all maps from $M_n(F)$ to itself satisfying A - ${\lambda}B{\in}{\Gamma}_n(F)$ if and only if ${\phi}(A)$ - ${\lambda}{\phi}(B){\in}{\Gamma}_n(F)$ for every A, $B{\in}M_n(F)$ and ${\lambda}{\in}F$. It was showed that ${\phi}{\in}{\Phi}_n(F)$ if and only if there exist an invertible matrix $P{\in}M_n(F)$ and an involutory element ${\varepsilon}$ such that either ${\phi}(A)={\varepsilon}PAP^{-1}$ for every $A{\in}M_n(F)$ or ${\phi}(A)={\varepsilon}PA^{T}P^{-1}$ for every $A{\in}M_n(F)$. As an application, the maps preserving inverses of matrces also are characterized.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.253-261
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• 2014

In this paper, we first will show that for any space X and any Wallman sublattice $\mathcal{A}$ of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}$, (${\Phi}^{-1}_{\mathcal{A}}(X)$, ${\Phi}_{\mathcal{A}}$) is the minimal quasi-F cover of X if and only if (${\Phi}^{-1}_{\mathcal{A}}(X)$, ${\Phi}_{\mathcal{A}}$) is a quasi-F cover of X and $\mathcal{A}{\subseteq}\mathcal{Q}_X$. Using this, if X is a locally weakly Lindel$\ddot{o}$f space, the set {$\mathcal{A}|\mathcal{A}$ is a Wallman sublattice of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}$ and ${\Phi}^{-1}_{\mathcal{A}}(X)$ is the minimal quasi-F cover of X}, when partially ordered by inclusion, has the minimal element $Z(X)^{\sharp}$ and the maximal element $\mathcal{Q}_X$. Finally, we will show that any Wallman sublattice $\mathcal{A}$ of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}{\subseteq}\mathcal{Q}_X$, ${\Phi}_{\mathcal{A}_X}:{\Phi}^{-1}_{\mathcal{A}}(X){\rightarrow}X$ is $z^{\sharp}$-irreducible if and only if $\mathcal{A}=\mathcal{Q}_X$.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.649-655
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• 1996

A positive, disjoint linear map $\phi : A \to B$ of C^*$-algebras preserves absolute values if any *-anti-homomorphism $\psi : A \to B$ is skew-hermitian with respect to every commutators of unitary elements.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.793-798
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• 2013

Let ${\phi}$ be a map of a manifold M into another manifold N, L(N) the bundle of all linear frames over N, and ${\phi}^{-1}$(L(N)) the bundle over M which is induced from ${\phi}$ and L(N). Then, we construct a structure equation for the torsion form in ${\phi}^{-1}$(L(N)) which is induced from a torsion form in L(N).

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.813-821
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• 2010

Let G and H be compact connected Lie groups with biinvariant Riemannian metrics g and h respectively, ${\phi}$ a group isomorphism of G onto H, and $E:={\phi}^{-1}TH$ the induced bundle by $\phi$ over the base manifold G of the tangent bundle TH of H. Let ${\nabla}$ and $^H{\nabla}$ be the Levi-Civita connections for the metrics g and h respectively, $\tilde{\nabla}$ the induced connection by the map ${\phi}$ and $^H{\nabla}$. Then, a necessary and sufficient condition for $\tilde{\nabla}$ in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) to be a Yang- Mills connection is the fact that the Levi-Civita connection ${\nabla}$ in the tangent bundle over (G, g) is a Yang- Mills connection. As an application, we get the following: Let ${\psi}$ be an automorphism of a compact connected semisimple Lie group G with the canonical metric g (the metric which is induced by the Killing form of the Lie algebra of G), ${\nabla}$ the Levi-Civita connection for g. Then, the induced connection $\tilde{\nabla}$, by ${\psi}$ and ${\nabla}$, is a Yang-Mills connection in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) over the base manifold (G, g).

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.329-337
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• 2016

In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman compactification of the inverse image ${\Phi}_K^{-1}(X)$ of the space X under the covering map ${\Phi}_K:QFK{\rightarrow}K$. Using these, we show that for any space X, ${\beta}QFX=QF{\beta}{\upsilon}X$ and that a realcompact space X is a projective object in the category $Rcomp_{\sharp}$ of all realcompact spaces and their $z^{\sharp}$-irreducible maps if and only if X is a quasi-F space.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.49-60
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• 2000

We will characterize isomorphisms from the adjoint of a certain tridiag-onal algebra $AlgL_{2n}$ onto $AlgL_{2n}$. In this paper the following are proved: A map $\Phi{\;}:{\;}(AlgL_{2n})^{*}{\;}{\longrightarrow}{\;}AlgL_{2n}$ is an isomorphism if and only if there exists an operator S in $AlgL_{2n}$ with all diagonal entries are 1 and an invertible backward diagonal operator B such that ${\Phi}(A){\;}={\;}SBAB^{-1}S^{-1}$.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.829-832
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• 1999

This to correct Section 4 of our previous work [1].