query: Dual of l_inf space of bounded sequences in R
positive_passages.docid: 111128
positive_passages.text: The Duals of $l^\infty$ and $L^{\infty}$
negative_passages.docid: 21070
negative_passages.text: Lim inf with norm and weak convergence
negative_passages.docid: 23076
negative_passages.text: Proof of limit of quotient sequence property
negative_passages.docid: 53363
negative_passages.text: Ultralimit of an eventually constant generalized sequence
negative_passages.docid: 59289
negative_passages.text: Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
negative_passages.docid: 119858
negative_passages.text: Proof: Every convergent sequence of real numbers is bounded
negative_passages.docid: 143424
negative_passages.text: Sequence problem involving inequalities
negative_passages.docid: 29655
negative_passages.text: $L^p$ and $L^q$ space inclusion
negative_passages.docid: 46892
negative_passages.text: Inclusion of $L^p$ spaces
negative_passages.docid: 57609
negative_passages.text: Hahn-Banach proof by extension of basis
negative_passages.docid: 133707
negative_passages.text: Notions of strong and weak convergence for $L^{2}(\mathbb R, \lambda)$ where $f_{n}(x)=1_{[n,n+1]}(x)$
negative_passages.docid: 81112
negative_passages.text: Proving that the dual of the $\mathcal{l}_p$ norm is the $\mathcal{l}_q$ norm.
negative_passages.docid: 13827
negative_passages.text: Uniform convergence for sequences of functions
negative_passages.docid: 146839
negative_passages.text: Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
negative_passages.docid: 73080
negative_passages.text: Is the set of all bounded sequences complete?
negative_passages.docid: 124959
negative_passages.text: Does weak compactness imply boundedness in a normed vector space (not necessarily complete)?
negative_passages.docid: 80276
negative_passages.text: Metric Space & Cauchy Sequence