Van Persie left Arsenal because of a difference in vision between himself and Wenger and Ivan Gazidis. RVP wants to win trophies, Champions League, Premiership etc. Arsenal couldn't demonstrate that commitment by investing in top quality players so he left. To put it bluntly, Wenger is a tight miser. He had money from the sale of Fabregas, Toure, Clichy and Nasri but chose not to spend. Walcott will be the next to leave.
And no disrespect to Giroud and Podolski but they are no replacement for RVP. The £230,000 he will be getting paid per week at Man U was also a nice sweetener but not the primary reason for his move.
Another trophy-less season beacons for Arsenal I'm afraid.