%0 Journal Article %T A note on lifting projections %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Hadwin, D. %D 2015 %\ 12/01/2015 %V 41 %N Issue 7 (Special Issue) %P 117-122 %! A note on lifting projections %K C*-algebra %K projection %R %X Suppose $\pi:\mathcal{A}\rightarrow \mathcal{B}$ is a surjective unital $\ast$-homomorphism between C*-algebras $\mathcal{A}$ and $\mathcal{B}$, and $0\leq a\leq1$ with $a\in  \mathcal{A}$. We give a sufficient condition that ensures there is a proection $p\in \mathcal{A}$ such that $\pi \left( p\right) =\pi \left( a\right) $. An easy consequence is a result of [L. G. Brown and G. k. Pedersen, C*-algebras of real rank zero, \textit{J. Funct. Anal.} {99} (1991) 131--149] that such a $p$ exists when $\mathcal{A}$ has real rank zero. %U http://bims.iranjournals.ir/article_727_582e0ada23e3758cdf98387770deec3b.pdf