• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.527-538
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• 2014

Let K be a compact Hausdorff space, $\mathfrak{A}$ a commutative complex Banach algebra with identity and $\mathfrak{C}(\mathfrak{A})$ the set of characters of $\mathfrak{A}$. In this note, we study the class of functions $f:K{\rightarrow}\mathfrak{A}$ such that ${\Omega}_{\mathfrak{A}}{\circ}f$ is continuous, where ${\Omega}_{\mathfrak{A}}$ denotes the Gelfand representation of $\mathfrak{A}$. The inclusion relations between this class, the class of continuous functions, the class of bounded functions and the class of weakly continuous functions relative to the weak topology ${\sigma}(\mathfrak{A},\mathfrak{C}(\mathfrak{A}))$, are discussed. We also provide some results on its completeness under the norm defined by ${\mid}{\parallel}f{\parallel}{\mid}={\parallel}{\Omega}_{\mathfrak{A}}{\circ}f{\parallel}_{\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.471-478
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• 2002

Let $Let\eta={\eta m}m$ be an eventually constant sequence of unit vectors $\eta m$ in $C^{n}$ and let $\rho$η be the pure state on $UHF_{n}$ algebra which is defined by $\rho\eta(\upsilon_i_1....\upsilon_i_k{\upsilon_{j1}}^*...{\upsilon_{j1}}^*)={\eta_1}^{i1}...{\eta_k}^{ik}{\eta_k}^{jk}...{\eta_1}^{j1}$. We find infinitely many state extensions of $\rho\eta$ to Cuntz algebra $O_n$ using representations and unitary operators. Also, we present theirconcrete expressions.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.117-132
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• 2011

By developing a linear algebra program involving many different structures associated to a three-graded H*-algebra, it is shown that if L is a Lie triple automorphism of an infinite-dimensional topologically simple associative H*-algebra A, then L is either an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism. If A is finite-dimensional, then there exists an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism F : A $\rightarrow$ A such that $\delta$:= F - L is a linear map from A onto its center sending commutators to zero. We also describe L in the case of having A zero annihilator.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.149-161
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• 2010

We adopt the idea of $C{\breve{a}}dariu$ and Radu to prove the generalized Hyers-Ulam stability of generalized Jordan triple derivation in Banach algebra. In addition, we take account of problems for generalized Jordan triple linear derivation in Banach algebra.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.487-497
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• 2020

In this paper, we establish a complex matrix representation of the Clifford algebra Cℓ_p,q. The size of our representation is significantly smaller than the size of the elements in L_p,q(ℝ). Additionally, we give detailed information about the spectrum of the constructed matrix representation.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.165-170
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• 2018

In this paper, we show that every unital n-Jordan homomorphism ${\varphi}$ from a Banach algebra ${\mathcal{A}}$ onto a semisimple commutative Banach algebra B is continuous.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.57-64
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• 2022

In this paper, we show, among others, that if A is a Banach algebra satisfying a functional identity involving a b-generalized derivation F on A, under some mild conditions, is of the form F(x) = ax for all x ∈ R, where a ∈ Q_r, a right Martindale quotient ring of A.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.395-401
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• 1997

We show that if I is an ideal of a $C^*$-algebra A such that the unitary group of I is connected then cer(A) $\leq$ cer(I) + cer(A/I), where cer(A) denotes the $C^*$-exponential rank of A.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.203-219
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• 2007

We estimate the stable rank and connected stable rank of group $C^*$-algebra of certain disconnected solvable Lie groups such as semi-direct products of connected solvable Lie groups by the integers.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.525-533
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• 1997

We analysis spectral subspaces of $C^*$-algebras for a compacr group action. And we prove the condition that the fixed point algebra of the product action is the tensor product of the fixed point algebras.