In finite dimensions, a matrix can be decomposed into the sum of rank-1 matrices. This got me thinking - in what situations can a bounded linear operator mapping between infinite dimensional spaces be written as an (infinite) sum of rank-1 operators?(adsbygoogle = window.adsbygoogle || []).push({});

eg, let A be a bounded linear operator from banach spaces X to Y, then perhaps we might try

[tex]A = \sum_{i=1}^\infty y_i \phi_i[/itex]

for some functionals [itex]\phi_i[/itex] in X', and elements y_i in Y.

Is there anything to this idea?

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# Linear operator decomposition

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