Yes. As Lyricist points out, a partial vacuum.
As humber points out below, its a surface area/volume ratio dilemma, as so many are.
As radius increases, the vol/surface area ratio gets much friendlier...but does it make analogous demands on the structural requirements?
In other words, is bigger better? Me thinks so. Yet, at a certain size, the weight of the atmosphere becomes an issue...more at the bottom of the balloon than at the top. This is assuming a crude geodesic sphere. Unlike a membrane without an underlying structure, the vacuum balloon would presumably remain roughly spherical.
Good architecture would allow for this anomaly; struts would be sized for the zone of air pressure they were exposed to.
At radius of 1/2 mile, for instance, if all the air could be removed, the weight removed would allow the floating of 1' or more of reinforced concrete.
This is clearly not do-able, as per limits of materials; expansion/contraction coefficients, etc, etc.
I've gone off topic, but hopefully its a welcome respite from the pointless bickering.
Risking more off-topic scolding, I wonder if spork and Tad have ever pondered the vacuum balloon?
I've been thinking about it , off and on, for 40 years.
(Not proud of that either...my wife wants me to mow the lawn and so forth.)