Re: Banach space Of Analytic Functions

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 12/18/04

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    Date: 18 Dec 2004 08:30:35 -0500

    On 17 Dec 2004 09:15:01 -0500, G A Edgar <edgar@math.ohio-state.edu>
    wrote:

    >On 16 Dec 2004 16:15:01 -0500, Ali Taghavi wrote:
    >>Of Course I Search for a NON STANDARD topology for some Functional
    >>Space(For Example schwars maps) which is invariant under the action
    >of
    >>a polynomial vector field X (As a Bounded operator )
    >
    >In a certain sense, such spaces have *only one* natural topology:
    >complete, separable, metrizable, and described without resort to the
    >Axiom of Choice. But I guess it takes a logician to specify what that
    >"sense" is.

    Someone might point out that the standard topology on the Schwarz
    space _is_ invariant under the action of a polynomial vector field
    (as a bounded operator) - it's just not given by a norm.

    ************************

    David C. Ullrich

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