PROOF
Print ISSN: 2944-9162, E-ISSN: 2732-9941 An Open Access International Journal of Applied Science and Engineering
Volume 5, 2025
Variable Exponential Lp(.) Operator Algebra Dynamical System
Author:
Abstract: Let (G, A, ω) be a variable exponential $$ L^{p(.)}$$ operator algebra dynamical system, let A be p(.) - incompressible. We establish that when $$ p(.) \in P(Ω)$$,
$$1< p_{m} \leq p(g) \leq p_{s}< \infty $$, $$g \in G$$ is not identical to 2 then mapping $$ Φ^{p(.)}$$ from $$ F^{p(.)} \left ( \hat{G}, F^{p(.)} (G,A,ω), \hat{ω} \right )$$ to LK $$ \left ( l^{p(.)} (G) \right ) \bigotimes p(.) $$ A is an isometric isomorphism if and only if the group G is finite. When G is finite then the isometric isomorphism $$ Φ^{p(.)}$$ is
equivariant for actions double dual actions: $$ \hat{\hat{ω}} : G \to F^{p(.)} (\hat{G}, F^{p(.)} (G, A, ω) \hat{ω})$$ and $$ ω \bigotimes Ad (ρ): G \to LK (l^{p(.)}(G)) \bigotimes p(.) A $$.
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Keywords: variable exponent Lebesgue space, Takai duality, spectral theory, variable exponential operator
crossed product, variable exponential operator algebra
Pages: 23-30
DOI: 10.37394/232020.2025.5.5