Given a weight function τ, we introduce new class of Banach algebras with respect to denoted by C_0b(X, τ ). We provide complete solution the isomorphism problem in this class. further characterize BSE-extension and Inoue-Doss ideal associated it. As an application our results, show equivalence four statements: (i) τ) is BSE, (ii) BED, (iii) Tauberian (iv) bounded.

LetG be a Polish group, τ a Polish topology on a spaceX, G acting continuously on (X, τ), with B ⊂ X G-invariant and in the Borel algebra generated by τ . Then there is a larger Polish topology τ ⊃ τ on X so that B is open with respect to τ, G still acts continuously on (X, τ), and τ has a basis consisting of sets that are of the same Borel rank as B relative to τ . 1

τ :−∞ x(τ)h(t− τ)dτ = x(t) = y(t) Note that i. Linearity justifies superposition principle; ii. Time-Invariance justifies the system’s response to δ(t − n∆τ) is h(t− n∆τ). iii. For time-varying systems, the system response to δ(t − n∆τ) becomes h(t, n∆τ), and y(t) = ∫ ∞ τ :−∞ x(τ)h(t, τ)dτ , where h(t, τ) is the system response at instant t to a unit impulse input located at τ . 3. [Convolution...

Given a von Neumann algebra M with a faithful normal semi-finite trace τ, we consider the non commutative Arens algebra Lω(M, τ) = ⋂ p≥1 Lp(M, τ) and the related algebras L2 (M, τ) = ⋂ p≥2 Lp(M, τ) and M + L2 (M, τ) which are proved to be complete metrizable locally convex *-algebras. The main purpose of the present paper is to prove that any derivation of the algebra M + L2 (M, τ) is inner and...

We have calculated the radiative corrections to the decay τ → π(K)ντ , taking to account internal bremsstrahlung and structure dependent radiation in the radiative decay and point meson, hadronic structure dependent and short distance contributions in the virtual corrections. We display the spectra of the photon energy and of the pion-photon invariant mass in the decay τ → πντγ and compare with...