Finite-rank Operator - Finite-rank Operators On A Banach Space

Finite-rank Operators On A Banach Space

A finite-rank operator between Banach spaces is a bounded operator such that its range is finite dimensional. Just as in the Hilbert space case, it can be written in the form

where now, and are bounded linear functionals on the space .

A bounded linear functional is a particular case of a finite-rank operator, namely of rank one.

Read more about this topic:  Finite-rank Operator

Famous quotes containing the word space:

    This moment exhibits infinite space, but there is a space also wherein all moments are infinitely exhibited, and the everlasting duration of infinite space is another region and room of joys.
    Thomas Traherne (1636–1674)