'The window must be open.'
Is this sentence correct?

According to my dictionary, when I use 'open' like this, as an predicate adjective,
the meaning is to run a shop or a bank.
Should I change 'open' to 'opened'?

And is 'Keep the window open.' correct?
Is this usage same with the above one?

Please tell me.
Yoko

"open" is a state (adj). "opened" is a form of the verb "to open".

An open window is a window which is open (not closed).

The window is open. (The window is not closed.)
Keep the window open. (Do not close it.)

The window is opened at 8 o'clock every morning. (Someone opens it every morning.)

Get into the elevator while the door is open. (while it is not closed)
The elevator door opened. (became open)

I opened the door. It is now open.

I had wrapped the packages neatly and left to go shopping. When I returned, I was surprised to find all the packages opened. (Out of curiosity, the children had opened them while I was away.)

In the preceding example, we must use "opened" for the packages, because packages are not the sort of thing that are naturally in either an open or closed state, like doors and windows and books.

There is room for disagreement on this last point, however, and there may be those who readily accept " ... find all the packages open".

The part about running a shop or bank didn't make sense to me, by the way. I don't know what your dictionary was trying to say by that.

Note that English does not have the equivalent distinctions for "closed", that is, there is no "close" meaning the opposite of "open". The window is closed.