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Equivalence constants for the $l_p$-norms and the $l_q$-symmetric multilinear operator norms of vectors in $\mathbb{C}^n$
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초록
We investigate the best equivalence constants for the $l_p$-norms and the $l_q$-symmetric multilinear operator norms of vectors in $\mathbb{C}^n$ which are induced by symmetric $n$-linear forms. In this paper, we provides estimates which are either best possible or close to best possible.
Abstract
We investigate the best equivalence constants for the $l_p$-norms and the $l_q$-symmetric multilinear operator norms of vectors in $\mathbb{C}^n$ which are induced by symmetric $n$-linear forms. In this paper, we provides estimates which are either best possible or close to best possible.
참고문헌 (5)
- S. Dineen, "Complex Analysis on Infinite-Dimensional Spaces, Springer Monographs in Mathematics" (1999), Springer-Verlag London, Ltd
- B. Q. Feng, "Equivalence constants for certain matrix norms", Linear Algebra Appl, 374, pp.247~253 (2003)[DOI]
- B. Q. Feng, "Equivalence constants for certain matrix norms. II", Linear Algebra Appl, 420(2-3), pp.388~399 (2007)[DOI]
- M. Goldberg, "Equivalence constants for lp norms of matrices", Linear and Multilinear Algebra, 21(2), pp.173~179 (1987)[DOI]
- A. Tonge, "Equivalence constants for matrix norms : a problem of Goldberg", Linear Algebra Appl, 306(1-3), pp.1~13 (2000)[DOI]
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