banach space in a sentence

Examples

1. Here c _ 0 is the Banach space of sequences converging to zero.
2. Suppose that and are Banach spaces and that.
3. For every separable Banach space, there is a closed subspace of such that.
4. Let be a linear mapping between Banach spaces.
5. Precisely, for every Banach space, the map
6. A Banach space isomorphic to is homogeneous, and Banach asked for the converse.
7. Hilbert spaces, Banach spaces or Fr�chet spaces.
8. Leonard Gross provided the generalization to the case of a general separable Banach space.
9. They are generalizations of Banach spaces ( normed vector spaces that are norm ).
10. In contrast to Banach spaces, the metric need not arise from a norm.