## Invertibility of linear combinations of two idempotents.(English)Zbl 1089.47002

Summary: Let $$P$$ and $$Q$$ be two idempotents on a Hilbert space. In this note, we prove that the invertibility of the linear combination $$\lambda_1P+\lambda_2Q$$ is independent of the choice of $$\lambda_i$$, $$i=1,2,$$ if $$\lambda_1\lambda_2\neq 0$$ and $$\lambda_1+\lambda_2\neq 0.$$

### MSC:

 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47L07 Convex sets and cones of operators

### Keywords:

Hilbert space; invertibility; linear combination
Full Text:

### References:

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