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I'm more wondering about the upper register here, but I suppose this applies to pedal notes also. Is the trumpet's range theoretically unlimited? Is there anything (besides the player) that potentially could limit the range of the trumpet?

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I'm guessing the physical size of the instrument will limit the minimum wavelength it can produce, and probably it would shatter or melt at a high enough frequency. Except for the fact that you probably can't put enough energy into it for that via any normal means, you just wouldn't get a sound out of it. – Matthew Read♦ Oct 12 '12 at 14:50

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As Matthew indicated in his comment, once the wavelength of the sound gets smaller than the diameter of the tubing, the trumpet will no longer behave like a column of air. This means that, at these wavelengths, the trumpet will not support the resonance modes that make up its behaviour at normal frequencies. I.e. not sound like a trumpet (to the extent that it sounds at all).

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