• Korean Journal of Mathematics
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• v.7 no.2
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• pp.219-226
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• 1999

In this paper, we discuss convergence theorem for exponentially bounded C-semigroups. We establish the convergence of the sequence of generators of exponentially bounded C-semigroups in some sense implies the convergence of the sequence of the corresponding exponentially bounded C-semigroups. Under the assumption that R(C) is dense, we show the equivalence between the convergence of generators and exponentially bounded C-semigroups.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.253-259
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• 2010

In this paper we establish approximation of contraction C-semigroups on the extrapolation space $X^C$, by showing the equicontinuity of contraction C-semigroups on $X^C$.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.139-146
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• 2000

In this paper, we discuss convergence theorem for contraction C-regularized semigroups. We establish the convergence of the sequence of generators of contraction regularized semigroups in some sense implies the convergence of the sequence of the corresponding contraction regularized semigroups. Under the assumption that R(C) is dense, we show the convergence of generators is implied by the convergence of C-resolvents of generators.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.111-119
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• 2022

In this article, we prove that diskcyclic C₀-semigroups exist on any infinite-dimensional Banach space. We show that a C₀-semigroup (T_t)_t≥0 satisfies the diskcyclicity criterion if and only if any of T_t's satisfies the diskcyclicity criterion for operators. Moreover, we show that there are diskcyclic C₀-semigroups that do not satisfy the diskcyclicity criterion. Also, we state various criteria for diskcyclicity of C₀-semigroups based on dense sets and d-dense orbits.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.401-409
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• 2004

In this paper, we show that C-resolvent of generator can be represented by Laplace transform and establish an exponential formula for C regularized semigroups whose antiderivatives are exponentially bounded.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1159-1172
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• 2019

A semigroup S is called a weakly abundant semigroup if its every $\tilde{\mathcal{L}}$-class and every $\tilde{\mathcal{R}}$-class contains an idempotent. Our purpose is to study an analogue of orthodox semigroups in the class of weakly abundant semigroups. Such an analogue is called a left quasi-abundant semigroup, which is a weakly abundant semigroup with a left quasi-normal band of idempotents and having the congruence condition (C). To build our main structure theorem for left quasi-abundant semigroups, we first give a sufficient and necessary condition of the idempotent set E(S) of a weakly abundant semigroup S being a left quasi-normal band. And then we construct a left quasi-abundant semigroup in terms of weak spined products. Such a result is a generalisation of that of Guo and Shum for left semi-perfect abundant semigroups. In addition, we consider a type Q semigroup which is a left quasi-abundant semigroup having the PC condition.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.115-121
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• 2001

In this paper, we establish the conditions that a mild C-existence family yields a solution to the abstract Cauchy problem. And we show the relation between mild C-existence family and C-regularized semigroup if the family of linear operators is exponentially bounded and C is a bounded injective linear operator.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.9-15
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• 1998

In this paper, we show convergence and approximation theorem for C-semigroups. And we study the problem of approximation of an exponentially bounded C-semigroup on a Banach space X by a sequence of exponentially bounded C-semigroup on $X_n$.

• East Asian mathematical journal
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• v.21 no.2
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• pp.151-161
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• 2005

We analyze the structure of $C^*-algebras$ generated by left regular isometric representations of semigroups.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.751-763
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• 2005

For a given gauge invariant state $\omega$ on the CAR algebra A isomorphic with the C$\ast$ -algebra of $2{\times}2$ complex matrices, we construct a family of quantum Markov semigroups on A which leave w invariant. By analyzing their generators, we decompose the algebra A into four eigenspaces of the semigroups and show some properties.