Definition:Invertible Bounded Linear Operator

This page is about invertibility in the context of Bounded Linear Operator. For other uses, see invertible.

Definition

Normed Vector Space

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

Let $T : X \to X$ be an invertible bounded linear transformation.

We say that $A$ is a bounded linear operator.

Inner Product Space

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

Let $T : X \to X$ be an invertible bounded linear transformation.

We say that $A$ is a bounded linear operator.

Also see

• Definition:Invertible Bounded Linear Transformation
• Definition:Inverse Linear Operator