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.

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