Yes, but I don't think we should be able to trade exotic and maybe not even legendary: I mean I know one guy who has 6 exotic weapons alone and I think it would decrease the value of finding something exotic. Furthermore the fact that glimmer is only used for a few things at higher levels means it's not a currency very fun to trade. I defiantly think all marks and currency should be assessable across characters though.
Also when using a trading system people can scam noobs out of really useful items! It just wouldn't be fair :/
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This could be some thing that bungie could add to destiny 2, think of swtor, there were so many varied items the game created its own successful and working economy, with global trade posts and ingame marketing. No real money of course😃