• 대한수학회보
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• 제61권3호
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• pp.813-823
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• 2024

In this paper, we prove that every 2-local derivation on several classes of C^*-algebras, such as unital properly infinite, type I or residually finite-dimensional C^*-algebras, is a derivation. We show that the following statements are equivalent: (1) every 2-local derivation on a C^*-algebra is a derivation, (2) every 2-local derivation on a unital primitive antiliminal and no properly infinite C^*-algebra is a derivation. We also show that every 2-local derivation on a group C^*-algebra C^*(𝔽) or a unital simple infinite-dimensional quasidiagonal C^*-algebra, which is stable finite antiliminal C^*-algebra, is a derivation.

• 대한수학회지
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• 제44권5호
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• pp.1185-1195
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• 2007

We will discuss some very old and some new open problems concerning infinite dimensional algebras. All these problems have been inspired by combinatorial group theory.

• 호남수학학술지
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• 제27권1호
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• pp.83-100
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• 2005

• 대한수학회논문집
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• 제9권4호
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• pp.847-852
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• 1994

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operator on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the ultraweak operator topology on $L(H)$.

• 대한수학회지
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• 제48권1호
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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.

• 대한수학회지
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• 제41권1호
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• pp.193-207
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• 2004

In this expository article we survey some recent developments on the construction of a holomorphic functional calculus for an infinite number of elements in a commutative unital Banach algebra.

• 대한수학회보
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• 제60권5호
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• pp.1221-1235
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• 2023

In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

• 대한수학회지
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• 제32권3호
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• pp.635-647
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• 1995

Let $H$ denote a separable, infinite dimensional complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $1_H$ and is closed in the $weak^*$ operator topology on $L(H)$. For $T \in L(H)$, let $A_T$ denote the smallest subalgebra of $L(H)$ that contains T and $1_H$ and is closed in the $weak^*$ operator topology.

• 대한수학회지
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• 제32권2호
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• pp.311-319
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• 1995

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operaors on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the $weak^*$ topology on $L(H)$. Note that the ultraweak operator topology coincides with the $weak^*$ topology on $L(H)$ (see [5]).

• 충청수학회지
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• 제8권1호
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• pp.137-145
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• 1995

In the white noise analysis the one-parameter groups play the powerful role. In this report, we will see a subgroup of infinite dimensional unitary group $U_{\infty}$ including guage transform and structure of this subgroup under the view point of Lie algebra.