$\|T\|= \sup_{\| f\|=1} |\langle Tf,f \rangle|$ for complex Hilbert spaces
55067
Norm of self-adjoint operator
12212
Showing a certain subspace of Hilbert space is dense
66409
Show that the linear operator $(Tf)(x)=\frac{1}{\pi} \int_0^{\infty} \frac{f(y)}{(x+y)} dy$ satisfies $\|T\|\leq 1$.
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
16692
a representation condition of Hilbert space
83360
The completion of a separable inner product space is a separable Hilbert space
95481
The set of self-adjoint operators over a Hilbert space doesn't form a lattice
118903
The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product
51302
Show that the operator norm is submultiplicative
27901
Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
36090
$TT^*=T^2$, show that $T$ is self-adjoint
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
2105
$\langle Tu\;|\;u\rangle=0,\;\forall u\in E \Longrightarrow T=0$?
2907
How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
133609
orthonormal system in a Hilbert space
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
136635
Proving that the Fourier Basis is complete for C(R/$2*\pi$ , C) with $L^2$ norm