• Communications of the Korean Mathematical Society
• /
• v.8 no.2
• /
• pp.225-231
• /
• 1993

• Bulletin of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.173-180
• /
• 1994

Let H be a separable, infinite dimensional, compled Hilbert space and let L(H) be the algebra of all bounded linear operators on H. A dual algebra is a subalgebra of L(H) that contains the identity operator $I_{H}$ and is closed in the ultraweak topology on L(H). Note that the ultraweak operator topology coincides with the wea $k^{*}$ topology on L(H)(see [3]). Bercovici-Foias-Pearcy [3] studied the problem of solving systems of simultaneous equations in the predual of a dual algebra. The theory of dual algebras has been applied to the topics of invariant subspaces, dilation theory and reflexibity (see [1],[2],[3],[5],[6]), and is deeply related with properties ( $A_{m,n}$). Jung-Lee-Lee [7] introduced n-separating sets for subalgebras and proved the relationship between n-separating sets and properties ( $A_{m,n}$). In this paper we will study the relationship between direct sum and properties ( $A_{m,n}$). In particular, using some results of [7] we obtain relationship between n-separating sets and direct sum of von Neumann algebras.ras.s.ras.

• Communications of the Korean Mathematical Society
• /
• v.10 no.4
• /
• pp.899-906
• /
• 1995

We discuss certain structure theorems in the class A which is closely related to the study of the problems of solving systems concerning the predual of a dual operator algebra generated by a contraction on a separable infinite dimensional complex Hilbert space.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.30 no.1C
• /
• pp.1-8
• /
• 2005

In this paper, we present a novel LDPC code construction called as semi-algebra low density parity check(LDPC) codes which is one kind of deterministic LDPC code based on dual-diagonal sub-matrix. The constructing method results in a class of high rate LDPC codes. Codes in this class have a large girth and good minimum distances. Furthermore, they can be implemented by simple parallel array architecture using cyclic shift register and perform well with the iterative decoding.

• Communications of the Korean Mathematical Society
• /
• v.9 no.4
• /
• pp.847-852
• /
• 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 $L(H)$.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.4
• /
• pp.613-629
• /
• 2016

In this paper, we introduced the notion of multiplier of Boolean algebras and discuss related properties between multipliers and special mappings, like dual closures, homomorphisms on B. We introduce the notions of xed set $Fix_f(X)$ and normal ideal and obtain interconnection between multipliers and $Fix_f(B)$. Also, we introduce the special multiplier ${\alpha}_p$a nd study some properties. Finally, we show that if B is a Boolean algebra, then the set of all multipliers of B is also a Boolean algebra.

• Kyungpook Mathematical Journal
• /
• v.47 no.2
• /
• pp.267-276
• /
• 2007

Injective JW-algebras are defined and are characterized by the existence of projections of norm 1 onto them. The relationship between the injectivity of a JW-algebra and the injectivity of its universal enveloping von Neumann algebra is established. The Jordan analgue of Theorem 3 of [3] is proved, that is, a JC-algebra A is nuclear if and only if its second dual $A^{**}$ is injective.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.1
• /
• pp.57-60
• /
• 2008

Let $U(sp_4)$ be the universal enveloping algebra of the symplectic Lie algebra $sp_4$. Then the restricted dual $U(sp_4)^{\circ}$ becomes a Poisson Hopf algebra with the Sklyanin Poisson bracket determined by the standard classical r-matrix. Here we illustrate a method to obtain the Lie bialgebra from a Poisson bialgebra $U(sp_4)^{\circ}$.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.727-739
• /
• 1998

We discuss dual algebras generated by a contraction and properties $({\mathbb}A_{m,n})$ which arise in the study of the problem of solving systems of the predual of a dual algebra. In particular, we study membership for the class ${\mathbb}A_1,{{\aleph}_0 }$. As some examples we consider dual algebras generated by a Jordan block.

• Journal of the Chungcheong Mathematical Society
• /
• v.17 no.1
• /
• pp.85-101
• /
• 2004

Let A be a Hopf algebra with a linear form ${\sigma}:k{\rightarrow}A{\otimes}A$, which is convolution invertible, such that ${\sigma}_{21}({\Delta}{\otimes}id){\tau}({\sigma}(1))={\sigma}_{32}(id{\otimes}{\Delta}){\tau}({\sigma}(1))$. We define Hopf algebras, ($A_{\sigma}$, m, u, ${\Delta}_{\sigma}$, ${\varepsilon}$, $S_{\sigma}$). If B and C are opposite skew copaired Hopf algebras and $A=B{\otimes}_kC$ then we find Hopf algebras, ($A_{[{\sigma}]}$, $m_B{\otimes}m_C$, $u_B{\otimes}u_C$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}B{\otimes}{\varepsilon}_C$, $S_{[{\sigma}]}$). Let H be a finite dimensional commutative Hopf algebra with dual basis $\{h_i\}$ and $\{h_i^*\}$, and let $A=H^{op}{\otimes}H^*$. We show that if we define ${\sigma}:k{\rightarrow}H^{op}{\otimes}H^*$ by ${\sigma}(1)={\sum}h_i{\otimes}h_i^*$ then ($A_{[{\sigma}]}$, $m_A$, $u_A$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}_A$, $S_{[{\sigma}]}$) is the dual space of Drinfeld double, $D(H)^*$, as Hopf algebra.