Can a security officer arrest a suspect for any misdemeanor that has been committed within his view or presence?

No

Another View: More specifics woujld have to be known. It can depend on what the security officer's powers may be under the laws of the jurisdiction he is working in. Some security officers actually carry commissions as Special Police Officers and ARE empowered to make arrests even for minor offenses.

Even though a private security officer is hired by a store or other business, they are still empowered to detain persons committing crime on the properties on which they are hired to protect.