Newbetuts

Show that $\exists L \in (l^\infty)'$ such that $\forall f \in C([0,1]): \int\limits_{0}^{1}f(t)dt = L(T(f))$.

$T$ is continuous $\iff \forall (x_1, x_2,..), x_i \in X, x_i \to^w x \implies T(x_i) \to^w T(x)$

Identification of $\ell_1^n$ $(\ell_\infty^n)$ with $\ell_\infty^{n^}$ $(\ell_1^{n^})$.

Are open balls in the topological dual space $A^$ weak- open?

Suppose $\forall x \in X,\sum_{n=1}^\infty|f_n(x)|<\infty$, to prove $\forall F\in X'', \sum_{n=1}^\infty |F(f_n)|\leq C\|F\|$.

Given a vector space $V$, why is the dual space $V^*$ interesting? [duplicate]

Is any Banach space a dual space?

Dual of $l^\infty$ is not $l^1$

Hahn-Banach theorem, dual space

Takesaki theorem 1.8: Is functional well-defined?

The dual space of $c$ is $\ell^1$

Why is there no natural isomorphism between $V$ and its dual?

Prove that $X^\ast$ separable implies $X$ separable

Why isn't lambda notation popular among mathematicians?

Motivation to understand double dual space

In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?

New posts in dual-spaces

$C(K)^*$ is not separable

How to interpret $(V^)^$, the dual space of the dual space?

$\nexists y \in l^1$ such that $\forall x \in S: L(x) = \sum\limits_{n\ge 1}(x y)\lbrack n \rbrack$

Separability of Banach Spaces

Show that $\exists L \in (l^\infty)'$ such that $\forall f \in C([0,1]): \int\limits_{0}^{1}f(t)dt = L(T(f))$.

$T$ is continuous $\iff \forall (x_1, x_2,..), x_i \in X, x_i \to^w x \implies T(x_i) \to^w T(x)$

Identification of $\ell_1^n$ $(\ell_\infty^n)$ with $\ell_\infty^{n^}$ $(\ell_1^{n^})$.

Are open balls in the topological dual space $A^$ weak- open?

Suppose $\forall x \in X,\sum_{n=1}^\infty|f_n(x)|<\infty$, to prove $\forall F\in X'', \sum_{n=1}^\infty |F(f_n)|\leq C\|F\|$.

Given a vector space $V$, why is the dual space $V^*$ interesting? [duplicate]

Is any Banach space a dual space?

Dual of $l^\infty$ is not $l^1$

Hahn-Banach theorem, dual space

Takesaki theorem 1.8: Is functional well-defined?

The dual space of $c$ is $\ell^1$

Why is there no natural isomorphism between $V$ and its dual?

Prove that $X^\ast$ separable implies $X$ separable

Why isn't lambda notation popular among mathematicians?

Motivation to understand double dual space

In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?