query: Prob. 10, Sec. 3.10 in Kreyszig's functional analysis book: Every isometric linear operator on a finite-dimensional inner product space is unitary?
positive_passages.docid: 158078
positive_passages.text: Is linear surjective isometry always unitary?
negative_passages.docid: 34173
negative_passages.text: Banach spaces and their unit sphere
negative_passages.docid: 125776
negative_passages.text: If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)
negative_passages.docid: 60934
negative_passages.text: What is a complex inner product space "really"?
negative_passages.docid: 20503
negative_passages.text: Meaning of inner product $\langle \vec{r} | \psi(t)\rangle $
negative_passages.docid: 89089
negative_passages.text: Prove that there is a unique inner product on $V$
negative_passages.docid: 128985
negative_passages.text: Show that $\langle x,y\rangle_A = \langle Ax,Ay\rangle$ is an inner product on $\mathbb R^n$
negative_passages.docid: 101861
negative_passages.text: How do you prove that $tr(B^{T} A )$ is a inner product?
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: 87580
negative_passages.text: Canonical examples of inner product spaces that are not Hilbert spaces?
negative_passages.docid: 55533
negative_passages.text: Tensor Product: Hilbert Spaces
negative_passages.docid: 125982
negative_passages.text: If the dual spaces are isometrically isomorphic are the spaces isomorphic?
negative_passages.docid: 43146
negative_passages.text: Does an integral operator with a symmetric integrable kernel have to be bounded on $L^2$?
negative_passages.docid: 119831
negative_passages.text: bounded operator $T$ is not compact then there exists an orthonormal sequence $e_n$ and $d>0$ such that $\|T(e_n)\|>d$ for all $n\in\Bbb{N}$?
negative_passages.docid: 62845
negative_passages.text: If two operators commute, does it mean that every eigenfuction of one is also an eigenfunction of the other?
negative_passages.docid: 11558
negative_passages.text: How to show that the limit of compact operators in the operator norm topology is compact
negative_passages.docid: 87897
negative_passages.text: Bounded operators on separable Hilbert spaces