Show that there exists $x \in H$ with $\|x\|=1$ and $|\langle Tx,x\rangle |=\|T\|$
55067
Norm of self-adjoint operator
133609
orthonormal system in a Hilbert space
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
111122
Proof of a theorem in Hilbert's system
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
6514
Prove $T$ has at most two distinct eigenvalues
31919
What can we say about the inner product $\langle f(t),f'(t) \rangle$?
111550
Let $A$ be a square complex matrix of size $n$ then $\langle Ax,x\rangle=0$ for $\forall x \in \Bbb C^n$ $\iff A=0$
118996
Prove that $T$ is an orthogonal projection
2105
$\langle Tu\;|\;u\rangle=0,\;\forall u\in E \Longrightarrow T=0$?
108837
How to show that $\vdash (\forall x \beta \to \alpha) \leftrightarrow \exists x (\beta \to \alpha)$?
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
134687
Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
80996
A canonical construction proving $\left|HK\right| = \left|H\right|\left|K\right| / \left|H \cap K\right|$?
141529
Proving existence of a minimum
129549
Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional
15262
Prove $\exists \xi, \eta \in (0,1)$, such that $f(\xi)+f'(\eta)=\xi+\eta$.