query: $\ell^p\!,$ for $p\neq2$, is not an inner product space.
positive_passages.docid: 144225
positive_passages.text: $\ell_p$ is Hilbert if and only if $p=2$
negative_passages.docid: 103460
negative_passages.text: Normal but not hermitian nor unitary
negative_passages.docid: 95513
negative_passages.text: Proving $W$ is a subspace of $P_{2}$
negative_passages.docid: 95601
negative_passages.text: Is the multiplication operator on $\ell^p$ compact?
negative_passages.docid: 64840
negative_passages.text: A Banach space that is not a Hilbert space
negative_passages.docid: 58009
negative_passages.text: How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
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
negative_passages.docid: 55864
negative_passages.text: Is there a null sequence that is in not in $\ell_p$ for any $p<\infty$?
negative_passages.docid: 14688
negative_passages.text: Do sequences in $\ell^p$ belong to some $\ell^q$ for $q<p$?
negative_passages.docid: 67383
negative_passages.text: Prove that $G'$ is not planar.
negative_passages.docid: 11710
negative_passages.text: How to show that $\mathbb{Q}$ is not $G_\delta$
negative_passages.docid: 132487
negative_passages.text: Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$
negative_passages.docid: 126927
negative_passages.text: $\mathbb Q$ is not the direct product of two non-trivial groups.
negative_passages.docid: 31002
negative_passages.text: Proving that the unit ball in $\ell^2(\mathbb{N})$ is non-compact
negative_passages.docid: 43826
negative_passages.text: Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
negative_passages.docid: 115272
negative_passages.text: Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
negative_passages.docid: 95481
negative_passages.text: The set of self-adjoint operators over a Hilbert space doesn't form a lattice