Results 141 to 150 of about 22,049 (161)
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Riesz-representable multilinear mappings
Linear and Multilinear Algebra, 2020We introduce the class of Riesz-representable multilinear mappings on products of L 1 ( μ ) spaces for finite measures μ and give their main properties.
Raffaella Cilia, Joaquín M. Gutiérrez
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Multilinear Maps and uniform boundedness
IEEE Transactions on Circuits and Systems, 1985The core of this excellent paper is the extension of the resonance theorem to multilinear operators. The proof ingeniously uses the well known linear version of this theorem. The paper considers more applications among which a significant one is the following: in the theory of Volterra truncated series representation of nonlinear systems (where the ...
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Almost p -summing polynomials and multilinear mappings
Archiv der Mathematik, 2001For a study of the injective maximal Banach operator ideal \(\Pi_{al,s}\) of almost summing operators see \textit{J. Diestel}, \textit{H. Jarchow} and \textit{A. Tonge} [``Absolutely Summing Operators'', Cambridge Studies, Adv. Math. 43 (1995; Zbl 0855.47016)].
Junek, Heinz +2 more
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Two applications of multilinear maps
Proceedings of the 2nd ACM workshop on ASIA public-key cryptography, 2014Constructing multilinear maps has been long-standing open problem, before recently the first construction based on ideal lattices has been proposed by Garg et al. After this breakthrough, various new cryptographic systems have been proposed. They introduce the concept of level into the encodings, and the system has a function that extracts a ...
Seiko Arita, Sari Handa
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On multilinear mappings attaining their norms.
Studia Mathematica, 1998The author proves that the set of bilinear continuous forms on a product of Banach spaces \(X\times Y\) whose third Arens transpose attains its norm is dense in the set of all bilinear continuous forms. Under certain assumptions on \(X\) and \(Y\), the author proves the density of those norm attaining maps which are weakly continuous on bounded sets ...
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On non-singular multilinear maps
Linear and Multilinear Algebra, 2010Let 𝕂 be a field and r 1, …, r t positive integers. Let r 1# ··· #r t be the smallest positive integer n for which there exists a non-singular multilinear map f : 𝕂 r 1 × ··· × 𝕂 r t → 𝕂 n . We show that for any field 𝕂, and the equality holds if 𝕂 is an algebraically closed field.
Xiaosong Sun, Xiankun Du, Dayan Liu
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Range Inclusion for Multilinear Mappings: Applications
Canadian Mathematical Bulletin, 1985AbstractThe result of S. Grabiner [5] on range inclusion is applied for establishing the following two theorems: 1. For A, B ∊ L(H), two operators on the Hilbert space H, we have DBC0(H) ⊆ DAL(H) if and only if DBC1(H) ⊆ DAL(H), where DA is the inner derivation which sends S ∊ L(H) to AS - SA, C1(H) is the ideal of trace class operators and C0(H) is ...
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Improvement of GGH Multilinear Map
2015 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC), 2015Garg, Gentry and Halevi (GGH) described the first candidate multilinear maps using ideal lattices. However, Hu and Jia presented an efficient attack on the GGH map, which breaks GGH-based MPKE. We describe an improvement of GGH map. The security of our construction depends upon new hardness assumption.
Chunsheng Gu +4 more
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Complexification of Multilinear Mappings and Polynomials
Mathematische Nachrichten, 2001Let \((X,\|\cdot\|_X)\) be a real normed space. The pair \((X_C,\gamma_C)\) is a complexification of \(X\) if \(X_C\) is the algebraic complexification of \(X\) and \(\gamma_C\) is a complex norm on \(X_C\) such that \(\gamma_C(x)=\|x\|_X\) for all \(x\in X\).
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