query: How to show that the canonical double-dual map $c_0\to\ell^\infty$ is not surjective?
positive_passages.docid: 132713
positive_passages.text: The space $c_0$ of sequences that converge to 0 is not reflexive
negative_passages.docid: 26110
negative_passages.text: Canonical isomorphism between $\mathfrak{so}(3)$ and $\mathbb R^3$ with vector cross product
negative_passages.docid: 86717
negative_passages.text: Completeness of $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle$
negative_passages.docid: 92497
negative_passages.text: Isometric Embedding of a separable Banach Space into $\ell^{\infty}$
negative_passages.docid: 93606
negative_passages.text: Showing that $C[0,1]$ is not complete
negative_passages.docid: 107682
negative_passages.text: Show that if the Riesz map is surjective on $H$, then $H$ is a Hilbert space
negative_passages.docid: 59929
negative_passages.text: Why is $(e_n)$ not a basis for $\ell_\infty$?
negative_passages.docid: 73573
negative_passages.text: image of polynomial map is not an algebraic set
negative_passages.docid: 80735
negative_passages.text: Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
negative_passages.docid: 98696
negative_passages.text: Is the exponential map ever not injective?
negative_passages.docid: 41620
negative_passages.text: The dual space of $c$ is $\ell^1$
negative_passages.docid: 5644
negative_passages.text: Is a right inverse of a surjective linear map linear?
negative_passages.docid: 63104
negative_passages.text: Dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$
negative_passages.docid: 65971
negative_passages.text: Double dual mappings
negative_passages.docid: 115999
negative_passages.text: Is there always an injective map from a space in its dual space?
negative_passages.docid: 85032
negative_passages.text: $Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
negative_passages.docid: 118903
negative_passages.text: The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product