continuous dual space造句

例句与造句

1. The article on dual spaces discusses the differences between the algebraic and the continuous dual spaces.
2. Further, for topological vector spaces, a continuous dual space can be defined, in which case a dual basis may exist.
3. To distinguish the ordinary dual space from the continuous dual space, the former is sometimes called the " algebraic dual ".
4. If we take " V * " to be the continuous dual space then it is the set of continuous linear functionals nonnegative on " C ".
5. It's mentioned on the page for dual spaces that if a vector space is topological, the continuous dual space is a linear subspace of the algebraic dual space.
6. It's difficult to find continuous dual space in a sentence. 用continuous dual space造句挺难的
7. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called the " continuous dual space ".
8. I got to thinking that it's probably true in general that if a space isn't locally convex, then it has to have a trivial continuous dual space.
9. This is in contrast to the case of the continuous dual space, discussed below, which may be isomorphic to the original vector space even if the latter is infinite-dimensional.
10. This space is called the dual space of " V ", or sometimes the "'algebraic dual space "', to distinguish it from the continuous dual space.
11. If there is no restriction to non-negative measures and complex measures are allowed, then Radon measures can be defined as the continuous dual space on the space of continuous functions with compact support.
12. When dealing with topological vector spaces, the definition is made instead for elements f _ j \ in ( V ^ \ prime ) ^ { \ otimes n }, the continuous dual space.
13. If one takes " F " to be the whole continuous dual space of " X ", then the weak topology with respect to " F " coincides with the weak topology defined above.
14. Thus the failure of some linear maps to be continuous for infinite-dimensional normed spaces implies that for these spaces, one needs to distinguish the algebraic dual space from the continuous dual space which is then a proper subset.
15. For a topological vector space V its " continuous dual space ", or " topological dual space ", or just " dual space " ( in the sense of the theory of topological vector spaces ) V'is defined as the space of all continuous linear functionals \ varphi : V \ to { \ mathbb F }.