Higher band gap in PL spectra then the UV visible spectroscopy calculated band gap
You don't give any details of the system you are studying - So, short answer... yes it is possible.
Such a system would be described as having an anti-Stokes shift, where the system emits a higher energy photon than the one(s) absorbed. This extra energy has to come from somewhere, and the typical scenarios for this include:
1) Emission after multiple photon absorptions (also called 'up-conversion' and can result in very large anti-Stokes shifts).
2) Absorption of a photon to give an excited state which then absorbs some vibrational energy from the lattice to give a higher energy excited state, which then emits a photon.
Fluorescence upconversion signal is the sum of two fluorescence beams, one from the sample itself (which is actual fluorescence of molecule) and one from the excitation source. Upconverted signal is not due to the relaxation of molecular excited state or you can not say that we have got higher optical band gap.
In case of two photon absorption, the absorption of second photon comes from a virtual excited state, and not from actual excited state (LUMO or S1).
So in both cases, the band gap of the molecule is same, as obtained by UV-visible spectroscopy.
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