Approximation numbers of matrix transformations and inclusion maps
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In this paper we establish relationships of the approximation numbers of matrix transformations acting between the vector-valued sequence spaces spaces of the type $\lambda(X)$ defined corresponding to a scalar-valued sequence space $\lambda$ and a Banach space $(X,\|.\|)$ as $$\lambda(X)=\{\overline x=\{x_i\}: x_i\in X, \forall~i\in \mathbb{N},~\{\|x_i\|_X\}\in \lambda\};$$ with those of their component operators. This study leads to a characterization of a diagonal operator to be approximable. Further, we compute the approximation numbers of inclusion maps acting between $\ell^p(X)$ spaces for $1\leq p\leq \infty$.
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2001 ◽
Vol 26
(11)
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pp. 671-678
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1995 ◽
Vol 18
(2)
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pp. 341-356
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1981 ◽
Vol 90
(1-2)
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pp. 63-70
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1986 ◽
Vol 100
(1)
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pp. 151-159
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1985 ◽
Vol 97
(1)
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pp. 137-146
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