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Martin Sleziak
Martin Sleziak
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Continuos Continuous differentiations of functional algebras

Latexing, fixing some font issues, minor grammar fixes
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user44191
user44191
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Let A is$A$ be some algebra (infinite-dimensional) of analytic functions on C^n. and D is$\mathbb{C}^n$, and $D$ be some differentiationderivation of A$A$, i.e. D(fg)=Df \cdot g +f \сdot Dg)$D(fg)=Df \cdot g + f \cdot Dg)$ (so A may be considered considered as a differential algebra).
When is this derivation is continuous (in some natural topology on A$A$)? Are there any useful sufficient conditions for the continuity of such derivations?

Let A is some algebra (infinite-dimensional) of analytic functions on C^n. and D is some differentiation of A i.e. D(fg)=Df \cdot g +f \сdot Dg) (so A may be considered as a differential algebra).
When this derivation is continuous (in some natural topology on A)? Are there any useful sufficient conditions for the continuity of such derivations?

Let $A$ be some algebra (infinite-dimensional) of analytic functions on $\mathbb{C}^n$, and $D$ be some derivation of $A$, i.e. $D(fg)=Df \cdot g + f \cdot Dg)$ (so A may be considered as a differential algebra).
When is this derivation continuous (in some natural topology on $A$)? Are there any useful sufficient conditions for the continuity of such derivations?

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Vladimir47
Vladimir47
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Continuos differentiations of functional algebras

Let A is some algebra (infinite-dimensional) of analytic functions on C^n. and D is some differentiation of A i.e. D(fg)=Df \cdot g +f \сdot Dg) (so A may be considered as a differential algebra).
When this derivation is continuous (in some natural topology on A)? Are there any useful sufficient conditions for the continuity of such derivations?