> No. T is the length of the OFDM symbol before the cyclic prefix has
> been added.

Umm, what part of what I wrote is no? I can define T how I like, and I
defined it to include the cyclic prefix. If there is no window applied
to the cyclic prefix, then the channel and the maths does not care
about the relative size of the original OFDM symbol and cyclic prefix?
A rect in the time domain is a sinc in the frequency domain. Where do
you think my logic is wrong?

But, I suppose that in the receiver the cyclic prefix gets removed
before the FFT demodulation. So as far as the FFT is concerned the
cyclic prefix was never there, so now the sub-carriers are spaced
closer together. Which raises the question, how does a
shaped(windowed) cyclic prefix help reduce inter-carrier interference
if it gets removed prior to the FFT demod? (I know the cyclic prefix
is added to allow for a guard interval, to deal with spread from one
OFDM symbol to the next. But I have also read papers describing how
the CP is also windowed such that it brings an advantage to the shape
of sub-carrier spectrum).

Regards
Andrew