If a Hilbert space is linearly isometric to a Banach space, will the Banach space be a Hilbert space?
97949
Existence of a $\mathbb C$-Banach space isometric to a Hilbert Space but whose norm is not induced by an inner product?
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
158082
Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
19294
‎If ‎‎$‎X$ is an infinite-dimensional Banach space and ‎‎$‎‎u‎\in ‎B(X)‎$ ,then $\bigcap_{v\in K(X)}\sigma(u+v) =\cdots$
107682
Show that if the Riesz map is surjective on $H$, then $H$ is a Hilbert space
14550
Every Hilbert space has an orthonomal basis - using Zorn's Lemma
132491
How to show that $C=C[0,1]$ is a Banach space
100161
Is it true that $\dim(X) \leq \dim(X^{\ast})$ for every infinite dimentional Banach space $X$?
96717
Hahn-Banach Theorem for separable spaces without Zorn's Lemma
97391
Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
38584
$T\colon L^2[0,1] \to L^2[0,1]$ be a bounded linear map of Hilbert spaces such that if $f\in L^2[0,1]$ is continuous then so is $Tf$.
145952
Example of a closed subspace of a Banach space which is not complemented?
90757
$T$ self-adjoint on Hilbert space $H$, $T^n=T^{n+1}$ will $T$ be an orthogonal projection operator?
3038
For positive invertible operators $C\leq T$ on a Hilbert space, does it follow that $T^{-1}\leq C^{-1}$?
116632
Gram-Schmidt in Hilbert space?
87580
Canonical examples of inner product spaces that are not Hilbert spaces?
129549
Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional