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

The Planck length as a duality of the Cosmological Constant: S-dS and S-AdS thermodynamics from a single expression