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Dual norm

About: Dual norm is a research topic. Over the lifetime, 740 publications have been published within this topic receiving 12304 citations.


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Journal ArticleDOI
Rob Stevenson1
TL;DR: An adaptive finite element method is constructed for solving elliptic equations that has optimal computational complexity and does not rely on a recurrent coarsening of the partitions.
Abstract: In this paper an adaptive finite element method is constructed for solving elliptic equations that has optimal computational complexity. Whenever, for some s > 0, the solution can be approximated within a tolerance e > 0 in energy norm by a continuous piecewise linear function on some partition with O(e-1/s) triangles, and one knows how to approximate the right-hand side in the dual norm with the same rate with piecewise constants, then the adaptive method produces approximations that converge with this rate, taking a number of operations that is of the order of the number of triangles in the output partition. The method is similar in spirit to that from [SINUM, 38 (2000), pp. 466-488] by Morin, Nochetto, and Siebert, and so in particular it does not rely on a recurrent coarsening of the partitions. Although the Poisson equation in two dimensions with piecewise linear approximation is considered, the results generalize in several respects.

467 citations

Journal ArticleDOI
TL;DR: It is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence.

364 citations

Journal ArticleDOI
TL;DR: In this article, the authors lay the foundations for a systematic study of tensor products of subspaces of C∗-algebras and employ various notions of duality.

311 citations

Journal ArticleDOI
TL;DR: In this article, the (n − 1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the derived norm is equivalent to those in the n − 1 norm.
Abstract: Given an n-normed space with n ≥ 2, we offer a simple way to derive an (n−1)- norm from the n-norm and realize that any n-normed space is an (n − 1)-normed space. We also show that, in certain cases, the (n − 1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the n-norm is equivalent to those in the derived (n − 1)-norm. Using this fact, we prove a fixed point theorem for some n-Banach spaces.

221 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202226
202114
202023
201915
201815