blob: cb1c44a4ec0c1d4778213b4f30fc30d68eea5f55 (
plain) (
blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
|
---
title: Quadratic Forms
parent: Unbounded Operators
nav_order: 5
published: false
description: >
The Hellinger–Toeplitz Theorem states that an everywhere-defined symmetric
operator on a Hilbert space is bounded. We give a proof using the Uniform
Boundedness Theorem. We give another proof using the Closed Graph Theorem.
---
# {{ page.title }}
{% definition Graph of an Operator %}
The *graph* of an operator $T$ in a Hilbert space $\hilb{H}$
is the set of all pairs $(x,y) \in \hilb{H}\times\hilb{H}$
where $x$ lies in the domain of $T$ and $y=Tx$.
{% enddefinition %}
|