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• W2009500549 abstract "A densely defined, closed linear operator F in a Hilbert space is said to be idempotent if ran(F)⊂dom(F) and F·F=F. We show that such an idempotent operator is written as F=P(P+Q)-1/2·(P+Q)-1/2 where P and Q are the orthoprojections to ran(F) and ker(F), respectively. When F is bounded, this becomes F=P(P+Q)-1. Further we show that for any λ≠0 the operator P+λQ is invertible and F=P(P+λQ)-1. In addition to the known results we present several descriptions of the norm ‖F‖ in terms of ‖P+Q‖,‖(P+Q)-1‖ or ‖(P-Q)-1‖." @default.
• W2009500549 created "2016-06-24" @default.
• W2009500549 creator A5006651719 @default.
• W2009500549 date "2013-05-01" @default.
• W2009500549 modified "2023-09-25" @default.
• W2009500549 title "Unbounded or bounded idempotent operators in Hilbert space" @default.
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• W2009500549 doi "https://doi.org/10.1016/j.laa.2011.06.047" @default.
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