## Monotonicity and $$^*$$orthant-monotonicity of certain maximum norms.(English)Zbl 1038.15017

Let $$\mathbb K$$ be the field of real or complex numbers. A characterization of all inner product norms $$p_1$$ and $$p_2$$ on $$\mathbb K^n$$ for which the norm $$x\mapsto \max\{ p_1(x),p_2(x)\}$$ on $$\mathbb K^n$$ is monotonic or *orthant-monotonic is given.

### MSC:

 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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### References:

 [1] Bauer, F.L; Stoer, J; Witzgall, C, Absolute and monotonic norms, Numer. math., 3, 257-264, (1961) · Zbl 0111.01602 [2] Clarke, F.H, Optimization and nonsmooth analysis, (1983), J. Wiley & Sons New York · Zbl 0727.90045 [3] Gries, D, Characterizations of certain classes of norms, Numer. math., 10, 30-41, (1967) · Zbl 0164.17603 [4] Johnson, C.R; Nylen, P, Monotonicity properties of norms, Linear algebra appl., 148, 43-58, (1991) · Zbl 0717.15015 [5] Lavrič, B, A note on ^{∗}orthant-monotonic norms, Linear algebra appl., 299, 195-200, (1999) · Zbl 0943.15018 [6] Rockafellar, T, Convex analysis, (1970), Princeton University Press Princeton, NJ · Zbl 0193.18401 [7] de Sá, E.M, Some notes on orthant-monotonic norms, Linear multilinear algebra, 32, 167-175, (1992) · Zbl 0757.15015 [8] de Sá, E.M; Sodupe, M.J, Characterizations of ^{∗}orthant-monotonic norms, Linear algebra appl., 193, 1-9, (1993) · Zbl 0793.15016
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