How to connect an HP External Monitor to MacBook Air via USB Port

I bought 2 adaptors, one from Anker and one from Hama. I can connect my HP external monitor directly on the USB Port of my mac book air but not through the adaptors. Both will not work. The same problem occurs with my external drive, a sandisk.

So both, Monitor and Sandisk will only work when they are directly connected in my macbook Air. Because I also need an Interface using USB 3, I simply cannot work....

Is there any adaptor REALLY working?

Any help highly welcome.

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