Fredholmness of linear combinations of two idempotents

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 Rakočević.

Original languageEnglish
Pages (from-to)579-583
Number of pages5
JournalIntegral Equations and Operator Theory
Issue number4
StatePublished - Dec 2007


  • Fredholm operator
  • Idempotent operator


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