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:
“No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being, because when any being is postulated, space is postulated.”
—Isaac Newton (1642–1727)