Fréchet algebras, formal power series, and automatic continuity

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Lie Algebras of Formal Power Series

Pseudodifferential operators are formal Laurent series in the formal inverse ∂−1 of the derivative operator ∂ whose coefficients are holomorphic functions. Given a pseudodifferential operator, the corresponding formal power series can be obtained by using some constant multiples of its coefficients. The space of pseudodifferential operators is a noncommutative algebra over C and therefore has a...

Automatic Continuity of Higher Derivations on JB*-Algebras

automatic continuity of homomorphisms between banach algebras and frechet algebras

Formal power series, operator calculus, and duality on Lie algebras

This paper presents an operator calculus approach to computing with non-commutative variables. First, we recall the product formulation of formal exponential series. Then we show how to formulate canonical boson calculus on formal series. This calculus is used to represent the action of a Lie algebra on its universal enveloping algebra. As applications, Hamilton's equations for a general Hamilt...