Wilson said he isn't concerned about Karlsson's health.
"That's the beauty in why it was so important to have the player here," he said. "We got to know him, not only as a person, but historically, the medical side of it. We're extremely comfortable. He went and had something that he was trying to play through fixed. It's going to be 100 percent come September, and he's putting the work in for that."
With Karlsson signed, the Sharks must turn its attention to other offseason questions, particularly regarding its depth at center.
They still have Logan Couture, who was third on the Sharks with 70 points (27 goals, 43 assists) in 81 games this season, and Tomas Hertl, who was second with 74 points (35 goals, 39 assists) in 77 games. But Joe Pavelski, who scored 38 goals and has been San Jose's captain since Oct. 5, 2015, could become an unrestricted free agent July 1, and Timo Meier, a 30-goal scorer, is a pending restricted free agent.
There is also the issue of whether Joe Thornton, who will turn 40 on July 2, will return for his 22nd NHL season. When Thornton does decide, Wilson said, "He'll call me and let me know. There'll always be a place for Joe Thornton in this organization, on or off the ice."
But after signing Karlsson, the Sharks are confident everything else will fall into place.
"To have three-high end defensemen (Burns, Karlsson, Marc-Edouard Vlasic), to be strong down the middle is really important. I think that's the foundation of any successful team," Wilson said. "Yes, you're going to have to integrate others in, you have to make decisions, but I tell you, knowing that we have this type of defense, knowing we have these types of centermen, it's a really good point to go forward and build our team off of."
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