In this work, we define a new style transfer task: perspective shift, which reframes a dialogue from informal first person to a formal third person rephrasing of the text. This task requires challenging coreference resolution, emotion attribution, and interpretation of informal text. We explore several baseline approaches and discuss further directions on this task when applied to short dialogues. As a sample application, we demonstrate that applying perspective shifting to a dialogue summarization dataset (SAMSum) substantially improves the zero-shot performance of extractive news summarization models on this data. Additionally, supervised extractive models perform better when trained on perspective shifted data than on the original dialogues. We release our code publicly.