# Category:Definitions/Bounded Linear Operators

This category contains definitions related to Bounded Linear Operators.
Related results can be found in Category:Bounded Linear Operators.

### Normed Vector Space

Let $\struct {V, \norm \cdot}$ be a normed vector space.

Let $A : V \to V$ be a linear operator.

We say that $A$ is a bounded linear operator if and only if:

there exists $c > 0$ such that $\norm {A v} \le c \norm v$ for each $v \in V$.

That is, a bounded linear operator on a normed vector space is a bounded linear transformation from the space to itself.

### Inner Product Space

Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space.

Let $\norm \cdot$ be the inner product norm for $V$.

Let $A : V \to V$ be a linear operator.

We say that $A$ is a bounded linear operator if and only if:

there exists $c > 0$ such that $\norm {A v} \le c \norm v$ for each $v \in V$.

That is, a bounded linear operator on an inner product space is a bounded linear transformation from the space to itself.

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Bounded Linear Operators"

The following 8 pages are in this category, out of 8 total.