I agree, that looks like typical spider mite damage. If you don't see any mites or their webs, then there's a high chance that the culprit is false spider mites (also called flat mites). They are microscopic in size (can't easily be seen with the naked eye) and don't make webs.
If only the one plant is affected, you can rub both sides of all the leaves with rubbing alcohol, it's usually quite effective. You will probably need to repeat this treatment a few times, every couple weeks. If the problem has spread to other plants, then chemical treatment may be needed.
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