"dedicated to" means "獻給"
"belonged" means "屬於"
To answer your question is both "yes" and "no". It will depend upon how you are going to use this museum for. If it is just to be a place that you own, then you can use "belonged". However, in your question, "...not getting the attention you deserve?", then you have to use "dedicated". If you read some of the book, at the beginning it will say something like:
I would like to dedicate this book to my wife (my children, my parents, my colleague...).
Because you want to use the museum to show people yourself. Therefore, it is better to use "dedicated" in this sentence. Basically, what I try to tell you is a logic. You need to based upon the logic of the sentence to determine which vocabulary is better to use.
By the way, it shall be "why not", not "why no" ...