• Communications of the Korean Mathematical Society
• /
• v.11 no.4
• /
• pp.1015-1030
• /
• 1996

We investigate complemented Banach subspaces of the Banach envelope of $eak L_1$. In particular, the Banach envelope of $weak L_1$ contains complemented Banach sublattices that are isometrically isomorphic to $l_p, (1 \leq p < \infty)$ or $c_0$. Finally, we also prove that the Banach envelope of $weak L_1$ contains an isomorphic copy of $l^{p, \infty}, (1 < p < \infty)$.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.537-545
• /
• 2007

We investigate complemented Banach sublattices of the Banach envelope of $Weak_L1$. In particular, the Banach envelope of $Weak_L1$ contains a complemented Banach sublattice that is isometrically isomorphic to a nonseparable Banach lattice $l_p(S),\;1{\leq}p<{\infty}\;and\;|S|{\leq}2^{{\aleph}0}$.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.3
• /
• pp.547-556
• /
• 2013

We investigate complemented Banach sublattices of the Banach envelope of $WeakL^1$. In particular, the Banach envelope of $WeakL^1$ contains a complemented Banach sublattice that is isometrically isomorphic to a separable reflexive Banach lattice.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.763-777
• /
• 2024

Let R be a commutative ring with identity 1≠ 0. In this paper, we continue the study started in [10] to further investigate when the extended zero-divisor graph of R, denoted as $\bar{\Gamma}$(R), is complemented. We also study when $\bar{\Gamma}$(R) is uniquely complemented. We give a complete characterization of when $\bar{\Gamma}$(R) of a finite ring R is complemented. Various examples are given using the direct product of rings and idealizations of modules.

• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.209-218
• /
• 2007

In this paper we investigate the ${\ell}^p$ space structure of the Banach envelope of $WeakL_1$. In particular, the Banach envelope of $WeakL_1$ contains a complemented Banach sublattice that is isometrically isomorphic to the nonseparable Banach lattice ${\ell}^p$, ($1{\leq}p<\infty$) as well as the separable case.

• Communications of the Korean Mathematical Society
• /
• v.18 no.3
• /
• pp.491-499
• /
• 2003

The Banach envelope of $WeakL_1$ contains a complemented Banach sublattice that is isometrically isomorphic to Lp($\mu$) space.

• Korean Journal of Mathematics
• /
• v.31 no.4
• /
• pp.385-389
• /
• 2023

In this article, we prove that an infinite dimensional complemented subspace X of 𝓛₁-space Z with unconditional basis (x_n) has the lifting property. Hence we can give an alternative proof that X is isomorphic to ℓ₁ given by Lindenstrauss and Pelczyński.

• Journal of the Korean BIBLIA Society for library and Information Science
• /
• v.1 no.1
• /
• pp.123-141
• /
• 1972

The Kosachalyo was the reference book which was composed of records collected about the procedures regulating the foreign relations or daily lives of the officials or the scholars, who had no official positions, in the Yi dynasty. The compilation work of the Kosachalyo was started from the date of the compilation of the original one by U sook-kwon (魚叔權) in the 9th year (1554) of King Myongjong (明宗). Su Myongung (徐明) revised and complemented the contents of the original one in full scale, named it as the Kosashinsu(攷事新書) in the 47th year(1771) of King Yongjo(英祖). In that period, the original Kosachalyo was revised and complemented twelve times and republished. Until now, it has been said that the original Kosachalyo had been suffered the revising or complementing works six times or nine times. But in this thesis it is assured that it was revised or complemented twelve times in the period from 1554 to 1771 upon the various historical documents.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.409-420
• /
• 1998

In this paper as a univesal Banach space of the separable Banach spaces we investigate the complemented Banach subspaces of $_wL_{\hat {I}}$. Also, using Peck's theorem and the properties of the envelope norm of $_wL_{\hat {I}}$ we will find a canonical basis of $l_1^n, l_\infty^n$ for each n.

• Korean Journal of Mathematics
• /
• v.27 no.3
• /
• pp.645-655
• /
• 2019

In this article, we show that the nuclear operator defined on Banach space has an extending and lifting operator. Also we give new proofs of the well known facts which were given $Pelcz{\acute{y}}nski$ theorem for complemented subspaces of ${\ell}_1$ and Lewis and Stegall's theorem for complemented subspaces of $L_1({\mu})$.