On Hermite interpolation in normed vector spaces

Normed Vector Spaces

A normed vector space is a real or complex vector space in which a norm has been defined. Formally, one says that a normed vector space is a pair (V, ∥ · ∥) where V is a vector space over K and ∥ · ∥ is a norm in V , but then one usually uses the usual abuse of language and refers to V as being the normed space. Sometimes (frequently?) one has to consider more than one norm at the same time; th...

متن کامل

Separation in General Normed Vector Spaces

The goal here is to extend this result to general normed vector spaces over the reals. Informally, a “vector space over the reals,” is a set X together with the operations vector addition and scalar multiplication, which are assumed to have the usual properties (e.g., vector addition is commutative). “Over the reals” means that scalars are in R rather than in some other field, such as the compl...

متن کامل

Normed Vector Spaces and Double Duals

In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by cons...

متن کامل

Normed Vector Spaces and Double Duals

In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by cons...

متن کامل

Normed Vector Spaces and Double Duals

In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by cons...

متن کامل

On Hermite interpolation in normed vector spaces

نویسندگان

چکیده

منابع مشابه

Normed Vector Spaces

Separation in General Normed Vector Spaces

Normed Vector Spaces and Double Duals

Normed Vector Spaces and Double Duals

Normed Vector Spaces and Double Duals

ژورنال