2013
DOI: 10.5186/aasfm.2013.3842
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Quasi s-numbers and measures of non-compactness of multilinear operators

Abstract: Abstract. The main goal of this paper is the study of quasi s-numbers of multilinear operators among Banach spaces. The relationships among multilinear variants of approximation, Kolmogorov and Gelfand numbers of operators and their generalized linear adjoint are shown. In the multilinear case, analogous theorems which are well-known in the linear case, are stated and proved. The estimates of measures of non-compactness of multilinear operators in terms of measures of the adjoint operators are also proved.

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Cited by 5 publications
(6 citation statements)
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“…By Lemma 8.5, there is R : Y → 2 such that R * = V . Thus, by [5,Proposition 3.2], we obtain a n (T × V ) = a n (T × R * ) = a n ((RT ) × ) ≤ a (k) n (RT ) ≤ sup{a (k) n (ST ); S : Y → 2 ≤ 1} = y (k) n (T ). (ii).…”
Section: Lemma 85mentioning
confidence: 99%
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“…By Lemma 8.5, there is R : Y → 2 such that R * = V . Thus, by [5,Proposition 3.2], we obtain a n (T × V ) = a n (T × R * ) = a n ((RT ) × ) ≤ a (k) n (RT ) ≤ sup{a (k) n (ST ); S : Y → 2 ≤ 1} = y (k) n (T ). (ii).…”
Section: Lemma 85mentioning
confidence: 99%
“…Now, we are ready to introduce a modified variant of the notion of s-numbers in the setting of k-linear operators, which appeared in [5].…”
Section: S-numbers Of Multilinear Operatorsmentioning
confidence: 99%
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“…Terzioğlu's characterization for compact maps found its use in more current research on compact maps as well. See [9,10,18].…”
Section: Corollary 25 ( [20])mentioning
confidence: 99%