• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.823-835
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• 2011

We investigate the continuity of (${\alpha},{\beta}$)-derivations on B(X) or $C^*$-algebras. We give some sufficient conditions on which (${\alpha},{\beta}$)-derivations on B(X) are continuous and show that each (${\alpha},{\beta}$)-derivation from a unital $C^*$-algebra into its a Banach module is continuous when and ${\alpha}$ ${\beta}$ are continuous at zero. As an application, we also study the ultraweak continuity of (${\alpha},{\beta}$)-derivations on von Neumann algebras.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.241-250
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• 2003

Let (B, m$_{B}$, k) be a maximal commutative $textsc{k}$-subalgebra of M$_{m}$(k). Then, for some element z $\in$ Soc(B), a k-algebra R = B［X,Y］/I, where I ＝ (m$_{B}$X, m$_{B}$Y, X$^2$- z,Y$^2$- z, XY) will create an interesting maximal commutative $textsc{k}$-subalgebra of a matrix algebra which is neither a $C_1$-construction nor a $C_2$-construction. This construction will also be useful to embed a maximal commutative $textsc{k}$-subalgebra of matrix algebra to a maximal commutative $textsc{k}$-subalgebra of a larger size matrix algebra.gebra.a.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.383-387
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• 2015

In [1], the definition of C*-Lie ternary (σ,τ,ξ)-derivation is not well-defined and so the results of [1, Section 4] on C*-Lie ternary (σ,τ,ξ)-derivations should be corrected.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.749-755
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• 2010

We investigate biprojectivity of $C_{r}^{*}(G)$ as a $L^1(G)$-bimodule for a locally compact group G. The main results are the following. As a $L^1(G)$-bimodule$C_{r}^{*}(G)$ is biprojective if G is compact and is not biprojective if G is an infinite discrete group or G is a non-compact abelian group.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.499-518
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• 1995

In this paper we consider more systematically the centralizer C(S) of the set $S = {f_a $\mid$ f_a : X \to X ; x \longmapsto x * a, a \in X}$ with respect to the semigroup End(X) of all endomorphisms of an implicative BCK-algebra X with the condition (S). We obtain a series of interesting results. The main results are stated as follows : (1) C(S) with repect to a binary operation * defined in a certain way forms a bounded implicative BCK-algebra with the condition (S). (2) X can be imbedded in C(S) such that X is an ideal of C(S)/ (3) If X is not bounded, it can be imbedded in a bounded subalgebra T of C(S) such that X is a maximal ideal of T. (4) If $X (\neq {0})$ is semisimple, C(S) is BCK-isomorphic to $\prod_{i \in I}{A_i}$ in which ${A_i}_{i \in I}$ is simple ideal family of X.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.61-80
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• 2013

In this paper, we study ${\alpha}$-completely positive maps between locally $C^*$-algebras. As a generalization of a completely positive map, an ${\alpha}$-completely positive map produces a Krein space with indefinite metric, which is useful for the study of massless or gauge fields. We construct a KSGNS type representation associated to an ${\alpha}$-completely positive map of a locally $C^*$-algebra on a Krein locally $C^*$-module. Using this construction, we establish the Radon-Nikod$\acute{y}$m type theorem for ${\alpha}$-completely positive maps on locally $C^*$-algebras. As an application, we study an extremal problem in the partially ordered cone of ${\alpha}$-completely positive maps on a locally $C^*$-algebra.

• Honam Mathematical Journal
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• v.4 no.1
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• pp.167-172
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• 1982

Let A be a Banach $^{\ast}$-algebra and C(t) be a closed $^{\ast}$-subalgebra of A gengerated by $t{\in}A$. A is locally $B^{\ast}$-equivalent [$B^{\ast}$-equivalent] if C(t) [A] for every hermitian element t is $^{\ast}$-isomorphic to some $B^{\ast}$-algebra. It was proved that the locally $B^{\ast}$-equivalent algebras with some conditions is $B^{\ast}$-equivalent by B. A. Barnes. In this paper, we obtain the some conditions for a locally $B^{\ast}$-equivalent algebra to be $B^{\ast}$-equivalent.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.59-63
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• 2003

Let A be a $C^*$-algebra and $K_{A}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\Gamma(K_{A})\;of\;K_{A}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\Gamma(K_{A})$.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1051-1068
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• 2015

We use methods of relative homological algebra on the category C(mod${\Lambda}$), of complexes of finitely generated modules over an artin algebra ${\Lambda}$, to give some characterizations of almost split sequences.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.443-447
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• 2001

The main goal of this paper is to show the following: Let d and g be (continuous or discontinuous) linear derivations on a Banach algebra A over a complex field C such that $\alphad^3+dg$ is a linear Jordan derivation for some $\alpha\inC$. Then the product dg maps A into the Jacobson radical of A.