• Title/Summary/Keyword: Isometrically isomorphic

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COMPLEMENTED SUBLATTICES OF $\omega L_i$ ISONMORPHIC TO CLASSICAL BANACH LATTICES

  • Kang, Jeong-Heung
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.1015-1030
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    • 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 $l^{p, \infty}, (1 < p < \infty)$.

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COMPLEMENTED SUBLATTICE OF THE BANACH ENVELOPE OF WeakL1 ISOMORPHIC TO ℓp

  • Kang, Jeong-Heung
    • Communications of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.209-218
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    • 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.

The Structure of Maximal Ideal Space of Certain Banach Algebras of Vector-valued Functions

  • Shokri, Abbas Ali;Shokri, Ali
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.189-195
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    • 2014
  • Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

NONSEPARABLE COMPLEMENTED SUBLATTICES IN THE BANACH ENVELOPE OF $WeakL_l$

  • Kang, Jeong-Heung
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.537-545
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    • 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 $l_p(S),\;1{\leq}p<{\infty}\;and\;|S|{\leq}2^{{\aleph}0}$.

Operators in L(X,Y) in which K(X,Y) is a semi M-ideal

  • Cho, Chong-Man
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.257-264
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    • 1992
  • Since Alfsen and Effors [1] introduced the notion of an M-ideal, many authors [3,6,9,12] have worked on the problem of finding those Banach spaces X and Y for which K(X,Y), the space of all compact linear operators from X to Y, is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y. The M-ideal property of K(X,Y) in L(X,Y) gives some informations on X,Y and K(X,Y). If K(X) (=K(X,X)) is an M-ideal in L(X) (=L(X,X)), then X has the metric compact approximation property [5] and X is an M-ideal in $X^{**}$ [10]. If X is reflexive and K(X) is an M-ideal in L(X), then K(X)$^{**}$ is isometrically isomorphic to L(X)[5]. A weaker notion is a semi M-ideal. Studies on Banach spaces X and Y for which K(X,Y) is a semi M-ideal in L(X,Y) were done by Lima [9, 10].

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A NOTE ON CERTAIN QUOTIENT SPACES OF BOUNDED LINEAR OPERATORS

  • Cho, Chong-Man;Ju, Seong-Jin
    • Communications of the Korean Mathematical Society
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    • v.19 no.4
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    • pp.715-720
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    • 2004
  • Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).