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PROPERTY T FOR FINITE VON NEUMANN ALGEBRAS
DEOK HOON BOO,CHUN-GIL PARK 충청수학회 1997 충청수학회지 Vol.10 No.1
We find more simple forms of property T for von Neumann algebras which are finite direct sum of II₁ factors.
STABILITY OF THE JENSEN'S EQUATION IN A HILBERT MODULE OVER A C<SUP>*</SUP>-ALGEBRA
Boo, Deok-Hoon,Park, Won-Gil 충청수학회 2002 충청수학회지 Vol.15 No.1
We prove the generalized Hyers-Ulam-Rassias stability of linear operators in a Hilbert module over a unital $C^*$-algebra.
A Note on Basic Construction and Index for Subfactors
Boo, Deok-Hoon 충청수학회 1990 충청수학회지 Vol.3 No.1
The converse of Pimsner-Popa theorem is proved, and represent the index [M : N] by finite sum of elements of M.
FUNCTIONAL EQUATIONS IN BANACH MODULES AND APPROXIMATE ALGEBRA HOMOMORPHISMS IN BANACH ALGEBRAS
Boo, Deok-Hoon,Kenary, Hassan Azadi,Park, Choonkil The Kangwon-Kyungki Mathematical Society 2011 한국수학논문집 Vol.19 No.1
We prove the Hyers-Ulam stability of partitioned functional equations in Banach modules over a unital $C^*$-algebra. It is applied to show the stability of algebra homomorphisms in Banach algebras associated with partitioned functional equations in Banach algebras.
Some Properties of Operators Which are Similar to Self-adjoint Operators
Boo, Deok-Hoon 충남대학교 자연과학연구소 1983 忠南科學硏究誌 Vol.10 No.2
Operator T에 대하여 아래의 사실들은 서로 동치임을 보였다. 1. 적당한 가역인 operator S에 대하여 S^-1 TS는 self-adjoint이다. 2. O??W(S) 가역인 operator S가 존재하여 TS=ST^*이다. 3. W(S)⊂{re^(iθ)|r>0}이고 가역인 operator S가 존재하여 TS=ST^*이다.
ON THE STRUCTURE OF NON-COMMUTATIVE TORI
Boo, Deok-Hoon,Park, Won-Gil 충청수학회 2000 충청수학회지 Vol.13 No.1
The non-commutative torus $A_{\omega}=C^*(\mathbb{Z}^n,{\omega})$ may be realized as the $C^*$-algebra of sections of a locally trivial $C^*$-algebra bundle over $\widehat{S_{\omega}}$ with fibres $C^*(\mathbb{Z}^n/S_{\omega},{\omega}_1)$ for some totally skew multiplier ${\omega}_1$ on $\mathbb{Z}^n/S_{\omega}$. It is shown that $A_{\omega}{\otimes}M_l(\mathbb{C})$ has the trivial bundle structure if and only if $\mathbb{Z}^n/S_{\omega}$ is torsion-free.
Primitive Ideal Spectrums of Inductive Limits of C^*-algebras
Boo, Deok-Hoon 충남대학교 자연과학연구소 1989 忠南科學硏究誌 Vol.16 No.2
C^*-bundle들의 inductive limit로 주어지는 C^*-bundle의 성질을 고찰하고, C^* 대수들의 inductive limit로 주어지는 C^*대수의 primitive ideal 스펙트럼이 Housdorff 공간이 되기 위한 조건을 찾아 보았다.
Continuity of homomorphisms between Banach algebras
Boo, Deok-Hoon 충남대학교 1985 忠南科學硏究誌 Vol.12 No.2
바나하 대수들의 집합 A와 B가 주어지고 A∈A에서 B∈B로 보내어지는 모든 준동형이 연속이면 B가 보다 큰 집합 B′로 확장되며, 또한 B′에서 quotient에 대해 닫혀 있기 위한 조건들을 살펴 보았다.
$C^*$-ALGEBRAS ASSOCIATED WITH LENS SPACES
Boo, Deok-Hoon,Oh, Sei-Qwon,Park, Chun-Gil Korean Mathematical Society 1998 대한수학회논문집 Vol.13 No.4
We define the rational lens algebra (equation omitted)(n) as the crossed product by an action of Z on C( $S^{2n+l}$). Assume the fibres are $M_{ k}$/(C). We prove that (equation omitted)(n) $M_{p}$ (C) is not isomorphic to C(Prim((equation omitted)(n))) $M_{kp}$ /(C) if k > 1, and that (equation omitted)(n) $M_{p{\infty}}$ is isomorphic to C(Prim((equation omitted)(n))) $M_{k}$ /(C) $M_{p{\infty}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p. It is moreover shown that if k > 1 then (equation omitted)(n) is not stably isomorphic to C(Prim(equation omitted)(n))) $M_{k}$ (c).
THE SPHERICAL NON-COMMUTATIVE TORI
Boo, Deok-Hoon,Oh, Sei-Qwon,Park, Chun-Gil Korean Mathematical Society 1998 대한수학회지 Vol.35 No.2
We define the spherical non-commutative torus $L_{\omega}$/ as the crossed product obtained by an iteration of l crossed products by actions of, the first action on C( $S^{2n+l}$). Assume the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus $A_{p}$ with a matrix algebra $M_{m}$ ( ) (m > 1). We prove that $L_{\omega}$/ $M_{p}$ (C) is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{mp}$ (C), and that the tensor product of $L_{\omega}$/ with a UHF-algebra $M_{p{\infty}}$ of type $p^{\infty}$ is isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) $M_{p{\infty}}$ if and only if the set of prime factors of m is a subset of the set of prime factors of p. Furthermore, it is shown that the tensor product of $L_{\omega}$/, with the C*-algebra K(H) of compact operators on a separable Hilbert space H is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) K(H) if Prim( $L_{\omega}$/) is homeomorphic to $L^{k}$ (n)$\times$ $T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.$T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.e.