normed space वाक्य
उदाहरण वाक्य
मोबाइल
- The converse is also true : if absolute convergence implies convergence in a normed space, then the space is a Banach space.
- This follows from the fact that for every normed space " Y ", separability of the continuous dual implies separability.
- I wish to prove that if X is a normed space, then every proper linear subspace V of X has empty interior.
- An important special case is the following : for every vector in a normed space, there exists a continuous linear functional on such that
- The Goldstine theorem states that the unit ball of a normed space is weakly *-dense in the unit ball of the bidual.
- The answer is, " not necessarily "; indeed, every infinite-dimensional normed space admits linear operators that are not closable.
- :* X is a normed space \ Longleftrightarrow X is a Banach space \ Longleftrightarrow X ^ \ star is a Smith space;
- A field with an absolute value or a normed space is either Archimedean or satisfies the stronger condition, referred to as the ultrametric triangle inequality,
- This general definition is convenient for defining a spatial median of a finite-dimensional normed space, for example, for distributions without a finite mean.
- The normed space " X " is uniformly smooth if and only if tends to 0 as " t " tends to 0.
- A normed space underlies an inner product space if and only if it satisfies the parallelogram law, or equivalently, if its unit ball is an ellipsoid.
- Note that each of the following objects is a special case of the types preceding it : normed spaces, Euclidean spaces, and the real / complex numbers.
- If and are normed spaces, they are "'isomorphic normed spaces "'if there exists a linear bijection such that and its inverse are continuous.
- If and are normed spaces, they are "'isomorphic normed spaces "'if there exists a linear bijection such that and its inverse are continuous.
- In particular, every continuous linear functional on a subspace of a normed space can be continuously extended to the whole space, without increasing the norm of the functional.
- It was simply referred to as property ( H ) in a list of properties for normed spaces that starts with ( A ) and ends with ( H ).
- A " linear transformation " between topological vector spaces, for example normed spaces, may be bounded, for example, when the domain is finite-dimensional.
- If the center is a distinguished point that is considered to be the origin of, as in a normed space, it is not mentioned in the definition and notation.
- This finite-dimensional version generalizes to functions & thinsp; and taking values in a normed space which could be for example a sequence space or an inner product space.
- Is a normed space but not an inner product space, because this norm does not satisfy the parallelogram equality required of a norm to have an inner product associated with it.
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