This will be a self-adjoint bounded linear operator with norm 9.

Thus, f is a bounded linear operator and so is continuous.

Let and suppose is a bounded linear operator for finite .

The bounded linear operators admit no everywhere defined traces.

Thus I defines a bounded linear operator from L(a,b) to itself.

Rather, a bounded linear operator is a locally bounded function.

The resolvent set of a bounded linear operator L is an open set.

For all locally convex spaces Y, every bounded linear operator from into is continuous.

A common procedure for defining a bounded linear operator between two given Banach spaces is as follows.

In fact every bounded linear operator on a complex Banach space must have a non-empty spectrum.

Let be a bounded linear operator.

This article will discuss the case where T is a bounded linear operator on some Banach space.

Many integral transforms are bounded linear operators.

Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.

Spectral theorem for bounded linear operators.

Theorem: Let T be a bounded linear operator from to and at the same time from to .

Such functions are important, for example, in constructing the holomorphic functional calculus for bounded linear operators.

The sum and the composite of two bounded linear operators is again bounded and linear.

Then P is a bounded linear operator if and only if the measure μ is Carleson.

A bounded linear operator between two Banach spaces is weakly compact if and only if it factors through a reflexive space.

If and are normal operators and if A is a bounded linear operator such that , then .

One of the open problems in functional analysis is to prove that every bounded linear operator on a Hilbert space has a proper invariant subspace.

Following the idea of Lumer, semi-inner-products were widely applied to study bounded linear operators on Banach spaces.

This correspondence between bounded linear operators and elements φ of the dual space of is an isometric isomorphism.

Thus a unitary operator is a bounded linear operator which is both an isometry and a coisometry.