https://shulchanaruchharav.com/halacha/scrubbing-shining-and-polishing/ according to this summary, there are some poskim who hold it prohibited in all cases to polish glass dishes on Shabbat, whereas some allow if one intends to use the dish on Shabbos. My question is, according to those opinions which permit, would it be permissible to polish a window on Shabbat? The reason I ask is, in this scenario the window has immediate use on Shabbos (for example, as a light source), but unlike plates and dishes which will inevitably get dirty, windows will most likely stay clean well into the week, and one would benefit from the cleaning during the week. So would this be an issue of doing something on Shabbat which will have benefit throughout the week, even if one gets immediate benefit?

According to this summary, there are some poskim who hold it prohibited in all cases to polish glass dishes on Shabbat, whereas some allow if one intends to use the dish on Shabbos. 

My question is, according to those opinions which permit, would it be permissible to polish a window on Shabbat? 

The reason I ask is, in this scenario the window has immediate use on Shabbos (for example, as a light source), but unlike plates and dishes which will inevitably get dirty, windows will most likely stay clean well into the week, and one would benefit from the cleaning during the week. So would this be an issue of doing something on Shabbat which will have benefit throughout the week, even if one gets immediate benefit?