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### How to construct an “explicit” element of $(\ell^\infty(\mathbb N))^* \setminus \ell^1(\mathbb N)$? [duplicate]

Possible Duplicate: Nonnegative linear functionals over $l^\infty$ An explicit functional in $(l^\infty)^*$ not induced by an element of $l^1$? Everything is in the title: How to construct an "...
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### An explicit functional in $(l^\infty)^*$ not induced by an element of $l^1$? [duplicate]

Possible Duplicate: Nonnegative linear functionals over $l^\infty$ Setup: Let $l^\infty$ be the set of bounded sequences (with terms in $\mathbb{R}$), and let $l^1$ be the set of sequences of ...
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### Existence of a $l_ {\infty} ^*$ element [duplicate]

Possible Duplicate: Nonnegative linear functionals over $l^\infty$ An explicit functional in $(l^\infty)^*$ not induced by an element of $l^1$? Exercise: Prove there exist a bounded linear ...
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### Generalized limit in $l_\infty$ (Using: Hahn Banach Extension Theorem)

I am trying to solve the following problem (found in Maddox's book "Elements of Functional Analysis", page 128): So we have the function $p:l_\infty\rightarrow\mathbb{R}$ given by  p(x) = \inf\...
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### Unbounded and linear transformation

I was thinking about this the other day. Does there exists any unbounded linear transformations from $\ell_\infty(\mathbb{R}) \to \mathbb{R}$ ? Here $\ell_\infty$ represent the infinity norm.
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### continuous linear functional on $l^{\infty}$ space
Let $l_{\infty}$ be the space of all bounded complex-valued sequences equipped with the supremum norm. Consider the natural standard basis $\{e_n\}_{n \in \mathbb{N}}$ of $l_{\infty}$. For any ...
### Exercise in Hahn-Banach Theorem; Finding linear functional $-p(-x)\leq f(x)\leq p(x)$
(The following exercises are in Kreyszig's book 218 page; EXE 10) I want to solve the following exercise : If $X=l^\infty$, let $p(x)=\lim\sup x_i$, which is sublinear. Then find a linear functional \$...