  In this paper we suggest that the Planck length $l_{pl}$ and the Cosmological
Constant scale $r_\Lambda=\frac{1}{\sqrt{\Lambda}}$ could in principle be dual
each other if we take seriously the so-called q-Bargmann Fock space
representation as has been previously suggested by Kempf and others and if
additionally we introduce $l_{pl}$ as an ultraviolet cut-off and
$r_\Lambda=\frac{1}{\sqrt{\Lambda}}$ as an infrared one. As a consequence, it
is possible to demonstrate that a Generalized Uncertainty Principle (GUP) given
by $\Delta X \Delta P\geq \frac{\hbar}{2}+\frac{l_{pl}^2}{2\hbar}(\Delta
P)^2+\frac{\hbar}{2r_\Lambda^2}(\Delta X)^2$, can reproduce appropriately the
thermodynamic behavior for both, the Schwarzschild Anti de-Sitter (S-AdS) and
the Schwarzschild de-Sitter (S-dS) space without making any analytic extension
for the coefficient (parameter) related to the minimum uncertainty in momentum
(already suggested in the literature). This is possible if the Black Hole
temperature is described with respect to the "natural" Static Observer for the
S-dS case located at a distance $l_0=(3/2r_s r_\Lambda^2)^{1/3}$.
