I looked up a trademark on TESS and it turns out that it is already trademarked. This may sound like a noob question, but can I use it if my business is completely unrelated ? What if I own the domain, but someone else owned the trademark.
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Yes, trademarks can be shared as long as they do not cause confusion.
For example,
Lexus the car Lexis the information service (Spelling is irrelevant in trademarks).
VAX a vacuum cleaner. VAX a computer
Which worked well until the vacuum cleaner started running ads "The VAX sucks."
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Ace Bandages and Ace Hardware. Delta Faucets and Delta Airlines.
Since these are in unrelated industries, there is no confusion. So, there is no infringement.
