Why is the Atlantic anticyclone an area of high pressure if it's the warmest spot on the planet?
The Bermuda high is centered near the horse latitudes, where air from the tropical Hadley trade wind cell is sinking. This forced sinking of air can dynamically contribute to high pressure even if the air is warm --- warm air can be forced to sink against its own buoyancy in a Ferrel-type circulation. But the Bermuda high is helped thermally too, at least in summer, because the Atlantic Ocean at those latitudes, at least in summer, is cooler than North America and much cooler than the Sahara at the same latitudes. It is certainly easier for a Ferrel-type circulation to work against cooler surface temperatures than against warmer ones.