SOME GENERALIZATIONS OF M-FINITE BANACH SPACES

Cha, Jae-Sun; Cha, Jae-Sun; Jung, Kap-Hun; Jung, Kap-Hun

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P-ISSN3059-0604
E-ISSN3059-1309
KCI

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Vol.3 No.2

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Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

1996, v.3 no.2, pp.155-162

Cha, Jae-Sun
Jung, Kap-Hun

Cha,, J. , & Jung,, K. (1996). , 3(2), 155-162.

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Abstract

We will show that let X and Y be M -finite Banach spaces with canonical M-decompositions $X{\cong}{{\prod}^{{\gamma}_{\infty}}_{i=1}}{X^{n_i}}_{i}\;and\;Y{\cong}{{\prod}^{{\bar{\gamma}}_{\infty}}_{j=1}}{\tilde{Y}^{m_j}}_{j}$, respectively and M and N nonzero locally compact Hausdorff spaces. Then I : $C_{0}$(M,X) ${\longrightarrow}\;C_{0}$(N,Y) is an isometrical isomorphism if and only if r = $\bar{r}$ and there are permutation and homeomorphisms and continuous maps such that I = ${I^{-1}}_{N.Y}\;{\circ}I_{w}^{-1}{\circ}({{\prod}^{\gamma}}_{i=1}I_{t_i,u_i}){\circ}I_{M,X}$.

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Article Contents

Vol.3 No.2

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics