במשך שבוע הוא היה בבית חולים.

English Translation

He was in the hospital for a week.

Why is ‘the hospital’ בית חולים rather than בית החולים?

In English, you can choose between “in the hospital”, “in a hospital”, or even “in hospital” to describe the same situation, depending on your frame of mind, emphasis, and other factors. For instance:

My husband is in the hospital. [Either he’s in a previously mentioned hospital, or he’s in some unnamed hospital.]
My husband is in a hospital. [He’s in some unnamed hospital.]
My husband is in hospital. [He’s in some unnamed hospital, and the speaker is not North American.]

It seems reasonable to assume something similar is true in Hebrew (with the exception that there are no different forms corresponding to “in a hospital” and “in hospital”).