@article{14ba353f07454361aedd63bbd70475de,

title = "Fredholmness of linear combinations of two idempotents",

abstract = "Let E and F be idempotent operators on a complex Hilbert space, and let a and b be nonzero scalars with a + b ≠ 0. We prove that aE + bF is Fredholm if and only if E + F is, thus answering affirmatively a question asked by Koliha and Rako{\v c}evi{\'c}.",

keywords = "Fredholm operator, Idempotent operator",

author = "Gau, {Hwa Long} and Wu, {Pei Yuan}",

note = "Funding Information: Proof. AsintheproofofTheorem1,E+F (resp.,E−F)isFredholmifandonlyif I−F11isinvertible,I−E31D1∗(I−F11)−1/2F11isFredholmanddimkerF2<∞1/2 (and, in addition, dim ker (I − F1) < ∞). Since ker (I − F1) = ran E ∩ ran F , the assertions in (a) and (b) follow easily. □ Acknowledgements. This research was partially supported by the National Science Council of the Republic of China under the research projects NSC 95-2115-M-008-011 and NSC 95-2115-M-009-001 of the two authors. The second author was also supported by the MOE-ATU project.",

year = "2007",

month = dec,

doi = "10.1007/s00020-007-1531-z",

language = "???core.languages.en_GB???",

volume = "59",

pages = "579--583",

journal = "Integral Equations and Operator Theory",

issn = "0378-620X",

number = "4",

}