query: A separable Banach space is isometrically isomorphic to a subspace of $\ell_{\infty}$
positive_passages.docid: 92497
positive_passages.text: Isometric Embedding of a separable Banach Space into $\ell^{\infty}$
negative_passages.docid: 64840
negative_passages.text: A Banach space that is not a Hilbert space
negative_passages.docid: 128866
negative_passages.text: Isomorphism between dual space and bilinear forms
negative_passages.docid: 9295
negative_passages.text: Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of X is uncountable.
negative_passages.docid: 41620
negative_passages.text: The dual space of $c$ is $\ell^1$
negative_passages.docid: 143517
negative_passages.text: Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
negative_passages.docid: 8334
negative_passages.text: A reflexive Banach space is separable iff its dual is separable
negative_passages.docid: 125073
negative_passages.text: Finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 125982
negative_passages.text: If the dual spaces are isometrically isomorphic are the spaces isomorphic?
negative_passages.docid: 134859
negative_passages.text: Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf implies that $X$ is separable.
negative_passages.docid: 26183
negative_passages.text: Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
negative_passages.docid: 7069
negative_passages.text: On the product of $\mathfrak c$-many separable spaces
negative_passages.docid: 59929
negative_passages.text: Why is $(e_n)$ not a basis for $\ell_\infty$?
negative_passages.docid: 46326
negative_passages.text: The space $C[a,b]$ with $\|f\|:=\int_a^b |f(x)|d(x)$ is a normed space but not a Banach space
negative_passages.docid: 127522
negative_passages.text: Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable
negative_passages.docid: 42108
negative_passages.text: Prove that $c_0$ is closed in $\ell^\infty$
negative_passages.docid: 156727
negative_passages.text: A step in the proof of Characterization of $W^{1,\infty}$