The concept should not be confused with that of a bounded operator.

It is also important when studying the spectrum of bounded operators.

This is not true for bounded operators in general.

Then T is also a bounded operator from to for any r between p and q.

Left multiplication by a fixed a A is a bounded operator.

The methods use the theory of bounded operators on Hilbert space.

The converse holds for bounded operators but fails in general.

For example, a bounded operator satisfying (9) is only quasinormal.

The compact operators form an important class of bounded operators.

His specialty is functional analysis, particularly bounded operators on a Hilbert space.

Note that the class of closed operators includes all bounded operators.

Such an operator is necessarily a bounded operator, and so continuous.

The space of bounded operators on does not have the approximation property (Szankowski).

The infinite matrix A with entries is a bounded operator on .

Compact operators form an ideal in the ring of bounded operators.

More generally, a bounded operator is quasiregular if -1 is not in its spectrum.

The generator of a uniformly continuous semigroup is a bounded operator.

Because of this property, the continuous linear operators are also known as bounded operators.

Closed operators are more general than bounded operators but still "well-behaved" in many ways.

First, it can be defined in a way analogous to how we define the adjoint of a bounded operator.

Every bounded operator becomes a contraction after suitable scaling.

Let be a Hilbert space and denote the set of all bounded operators on .

Let be the von Neumann algebra of bounded operators on for .

More generally, the set of invertible bounded operators on a (complex) Hilbert space is connected.

(a) A Hilbert space such that acts on it as an algebra of bounded operators.