We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.
@article{bwmeta1.element.bwnjournal-article-smv117i3p275bwm,
author = {Ian Doust and Byron Walden},
title = {Compact AC-operators},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {275-287},
zbl = {0851.47025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv117i3p275bwm}
}
Doust, Ian; Walden, Byron. Compact AC-operators. Studia Mathematica, Tome 119 (1996) pp. 275-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv117i3p275bwm/
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