query: In an inner product space, can we have $\langle\sum_{n=1}^\infty x_n,y\rangle=\sum_{n=1}^\infty\langle x_n,y\rangle$?
positive_passages.docid: 155479
positive_passages.text: Summation of inner products
negative_passages.docid: 37060
negative_passages.text: The Parallelogram Identity for an inner product space
negative_passages.docid: 71350
negative_passages.text: Let $H$ be a Hilbert space with projections $P,Q$, then $\lim_{n\to\infty}(PQ)^nx= Rx$ for all $x\in H$, where $R$ is the projection to $PH\cap QH$
negative_passages.docid: 115012
negative_passages.text: Klein-Gordon inner product
negative_passages.docid: 122121
negative_passages.text: Is there a vector space that cannot be an inner product space?
negative_passages.docid: 82464
negative_passages.text: $U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
negative_passages.docid: 105363
negative_passages.text: $\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
negative_passages.docid: 134687
negative_passages.text: Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
negative_passages.docid: 1751
negative_passages.text: When does the tensor product distribute over an infinite direct product?
negative_passages.docid: 69766
negative_passages.text: Is every normed vector space, an inner product space
negative_passages.docid: 146839
negative_passages.text: Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
negative_passages.docid: 63032
negative_passages.text: Why is it true that every finite-dimensional inner product space is a Hilbert space?
negative_passages.docid: 57619
negative_passages.text: Norms Induced by Inner Products and the Parallelogram Law
negative_passages.docid: 36142
negative_passages.text: What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
negative_passages.docid: 158082
negative_passages.text: Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
negative_passages.docid: 89089
negative_passages.text: Prove that there is a unique inner product on $V$
negative_passages.docid: 2105
negative_passages.text: $\langle Tu\;|\;u\rangle=0,\;\forall u\in E \Longrightarrow T=0$?