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.