How to unpublished a node from a view?
I suppose you could use Views Bulk Operations (VBO) to achieve this. VBO lets you select various nodes in a list and then perform an action to all of them. VBO is highly customizable and extendible. VBO can be combined with other modules like mighty Rules and others. Bulk publishing and  unpublishing would (of course) also be possible.

ps: actually this could also be achived through the 'regular' content handling (/admin/content). Just set the content type filter to your content type and you can already bulk publish/unpublish. But I suppose you tried this already and would prefer to have the same nodes as you have in the view?