• Title/Summary/Keyword: compact ideal

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HEREDITARY PROPERTIES OF CERTAIN IDEALS OF COMPACT OPERATORS

  • Cho, Chong-Man;Lee, Eun-Joo
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.3
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    • pp.457-464
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    • 2004
  • Let X be a Banach space and Z a closed subspace of a Banach space Y. Denote by L(X, Y) the space of all bounded linear operators from X to Y and by K(X, Y) its subspace of compact linear operators. Using Hahn-Banach extension operators corresponding to ideal projections, we prove that if either $X^{**}$ or $Y^{*}$ has the Radon-Nikodym property and K(X, Y) is an M-ideal (resp. an HB-subspace) in L(X, Y), then K(X, Z) is also an M-ideal (resp. HB-subspace) in L(X, Z). If L(X, Y) has property SU instead of being an M-ideal in L(X, Y) in the above, then K(X, Z) also has property SU in L(X, Z). If X is a Banach space such that $X^{*}$ has the metric compact approximation property with adjoint operators, then M-ideal (resp. HB-subspace) property of K(X, Y) in L(X, Y) is inherited to K(X, Z) in L(X, Z).

A NOTE ON M-IDEALS OF COMPACT OPERATORS

  • Cho, Chong-Man;Kim, Beom-Sool
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.683-687
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    • 1998
  • Suppose X is a subspace of $(\sum_{n=1} ^{\infty} X_n)_{c_0}$, dim $X_n<{\infty}$, which has the metric compact approximation property. It is proved that if Y is a Banach space of cotype q for some $2{\leq}1<{\infty}$ then K(X,Y) is an M-ideal in L(X,Y).

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On M-ideal properties of certain spaces of compact operators

  • Cho, Chong-Man;Kim, Beom-Sool
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.673-680
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    • 1996
  • It is proved that $K(c_0,Y)$ is an M-ideal in $L(c_0,Y)$ if Y is a closed subspace of $c_0$. And a new direct proof of the fact that $K(L_1[0,1],\ell_1)$ is not an M-ideal in $L(L_1[0,1],\ell_1)$ is given.

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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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Remarks on M-ideals of compact operators

  • Cho, Chong-Man
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.445-453
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    • 1996
  • A closed subspace J of a Banach space X is called an M-ideal in X if the annihilator $J^\perp$ of J is an L-summand of $X^*$. That is, there exists a closed subspace J' of $X^*$ such that $X^* = J^\perp \oplus J'$ and $\left\$\mid$ p + q \right\$\mid$ = \left\$\mid$ p \right\$\mid$ + \left\$\mid$ q \right\$\mid$$ wherever $p \in J^\perp and q \in J'$.

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ON THE SEPARATING IDEALS OF SOME VECTOR-VALUED GROUP ALGEBRAS

  • Garimella, Ramesh V.
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.737-746
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    • 1999
  • For a locally compact Abelian group G, and a commutative Banach algebra B, let $L^1$(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is noncompact and B is a semiprime Banach algebras in which every minimal prime ideal is cnotained in a regular maximal ideal, then $L^1$(G, B) contains no nontrivial separating idal. As a consequence we deduce some automatic continuity results for $L^1$(G, B).

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Fabrication of Hydroxyapatite Ceramics to Mimic the Natural Bone Structure

  • Moon, Dae-Hee;Ryu, Su-Chak
    • Journal of the Korean Ceramic Society
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    • v.48 no.5
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    • pp.390-395
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    • 2011
  • The objective of our study was to produce an imitation bone material consisting of hydroxyapatite with a compact and spongy structure. This study shows the ideal content of $SiO_2$ and the sintering temperature to produce imitation bone that has the mechanical properties of natural bone. On the basis of our determination of the ideal conditions, a compact part was produced and its mechanical properties were tested. A compact part made of 0.5 wt% $SiO_2$ and sintered at $1350^{\circ}C$ showed excellent mechanical properties. The bioactivity of the compact part under this condition was tested, and it was found to be bioactive. The porous part was produced by controlling the powder size, and the dual structure was manufactured by combining the compact and porous parts. A water permeability test confirmed that the dual structure had an interconnected pore structure. Therefore, this dual-body structure is feasible for use in the creation of implants.

APPROXIMATION IN LIPSCHITZ ALGEBRAS OF INFINITELY DIFFERENTIABLE FUNCTIONS

  • Honary, T.G.;Mahyar, H.
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.629-636
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    • 1999
  • We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

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Essentially normal elements of von neumann algebras

  • Cho, Sung-Je
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.653-659
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    • 1995
  • We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

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