科研之友
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摘要
If X is a real vector space and p an asymmetric norm on X, the set C-p = {x is an element of X: p(-x) = 0} is a proper cone in X which induces a partial order on X compatible. with the linear structure of X. Using the norm p(s)(x) = max{p(x),p(-x)}, a second asymmetric norm can be defined by q(p),(x) = inf{p(s)(x + y) : y is an element of C-p}. In the case where the partial order induced by G is a lattice order, it is possible to define a third asymmetric norm by p(+)(x) = p(x(+)), where x(+) is the positive part of x. The paper investigates the relationships between these three asymmetric norms, with special attention to the case where X is finite-dimensional.
- 出版日期2015-9-15
