Unexpected Uncertainty Principle for Disc Banach Spaces

Let (ₙ\ₙ₌₁^∞, \τₙ\ₙ₌₁^∞) and (ₙ\ₙ₌₁^∞, \ωₙ\ₙ₌₁^∞) be unbounded continuous p-Schauder frames ($0<p<1$) for a disc Banach space X. Then for every x ∈ ( D(θf) (θg))\0\, we show that {align}{UB} \|θ_f x\|_0\|θ_g x\|_0 ≥ {1}{(n,m ∈ N|f_n(ω_m)|)^p(n, m ∈ N|g_m(τ_n)|)^p}, {align} where {align*} & θ_f: D(θ_f) x ↦ θ_fx \{f_n(x)\}ₙ₌₁^∞∈ ^p(N), θ_g: D(θ_g) x ↦ θ_gx \{g_n(x)\}ₙ₌₁^∞∈ ^p(N). {align*} Inequality (1) is unexpectedly different from both bounded uncertainty principle [arXiv:2308.00312v1] and unbounded uncertainty principle [arXiv:2312.00366v1] for Banach spaces.