• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.895-908
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• 2016

Firstly, we establish spectral mapping theorems for normal eigenvalues (due to Browder) of a $C_0$-semigroup and its generator. Secondly, we discuss relationships between normal eigenvalues of the compact monodromy operator and the generator of the evolution semigroup on $P_{\tau}(X)$ associated with the ${\tau}$-periodic evolutionary process on a Banach space X, where $P_{\tau}(X)$ stands for the space of all ${\tau}$-periodic continuous functions mapping ${\mathbb{R}}$ to X.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.483-507
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• 2004

In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.97-107
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• 1999

Given a C-dynamical system (A, G, $\alpha$) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, $\alpha$) with a left-cancellative semigroup M with unit. We construct a new C-algebra A $\alpha$rM, the reduced crossed product of A by the semigroup M under the action $\alpha$ and investigate some properties of A $\alpha$rM.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.111-137
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• 2021

Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.753-759
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• 1995

Let C be a smooth complex algebraic curve of genus g. For a divisor D on C, dim D means the dimension of the complete linear series $\mid$D$\mid$ containing D, which is the same as the projective dimension of the vector space of meromorphic functions f on C with divisor of poles $(f)_\infty \leq D$.

• Bulletin of the Korean Mathematical Society
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• v.27 no.2
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• pp.157-164
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• 1990

The purpose of this paper is to consider the inhomogeneous initial value problem (Fig.) in a Banach space X, where Z is the generator of an exponentially bounded C-semigroup in X, f9t) : [0, T].rarw.X and x.mem.X. Davies-Pang [1] showed the corresponding homogeneous equation, this is, the equation with f(t).iden.0, has a unique solution depending continuoously on the initial value x.mem.CD(z) in the $C^{-1}$-graph norm on CD(Z) when T=.inf..

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.175-182
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• 2001

In this paper we prove the existence and uniqueness of a mild solution of a functional differential equation with nonlocal condition using the semigroup theory and the Banach fixed point principle.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1101-1110
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• 2023

At the present paper, we investigate bounded approximately local derivations of ℓ¹-Munn algebra 𝕄_I(𝒜), where I is an arbitrary non-empty set and 𝒜 is an approximately locally unital Banach algebra. Indeed, we show that if _𝒜B(𝒜, 𝒜^*) and B_𝒜(𝒜, 𝒜^*) are reflexive, then every bounded approximately local derivation from 𝕄_I(𝒜) into any Banach 𝕄_I(𝒜)-bimodule X is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra ℓ¹(S), where S is a uniformly locally finite inverse semigroup.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.185-191
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• 1997

The notions of implicative semigroup and ordered filter were introduced by M. W. Chan and K. pp. Shum [3]. The first is a generalization of implicative semilattice (see W. C. Nemitz [6] and T. S. Blyth [2]) and has a close relation with the implication in mathematical logic and set theoretic difference (see G. Birkhoff [1] and H. B. Curry [4]). For the general development of implicative semilattice theory the ordered filters play an important role, which is shown by W. C. Nemitz [6].

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.63-74
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• 2012

Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.