Built-in shelves brackets
That's an odd set, really.
The ends have to be &quot;floating&quot; to hold any weight, at which point the usual approach is to dispense with the uprights and make the shelves fully &quot;floating.&quot;
There are a few ways of floating shelves, all simple in concept but finicky in practice. One is long rods set into the studs (deeper than is safe if you don't know what's in the studs so you can miss wires and pipes) with matching holes in the back of the shelves. Conceptually simple, but if anything is the least bit at the wrong angle, very difficult in practice as the rods and holes won't line up and the shelves won't slide on.
Another approach uses a bracket that screws to the wall surface, and a shelf that's essentially a hollow box that slips over the bracket to hide it.