Auxiliary normed space
In functional analysis, two methods of constructing normed spaces from disks were systematically employed by Alexander Grothendieck to define nuclear operators and nuclear spaces. One method is used if the disk is bounded: in this case, the auxiliary normed space is with norm The other method is used if the disk is absorbing: in this case, the auxiliary normed space is the quotient space If the disk is both bounded and absorbing then the two auxiliary normed spaces are canonically isomorphic (as topological vector spaces and as normed spaces).
Auxiliary normed spacesBanach diskBornivorous setBornological spaceBounded completantFast convergenceFast convergent sequenceInductive tensor productInfracompleteInfracomplete spaceInjective tensor productIntegral linear operatorKatowice propertyMetrizable topological vector spaceNuclear operatorNuclear spacePolar topologyProjective tensor productSequentially completeTopological vector spaceUltrabornological space
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Auxiliary normed space
In functional analysis, two methods of constructing normed spaces from disks were systematically employed by Alexander Grothendieck to define nuclear operators and nuclear spaces. One method is used if the disk is bounded: in this case, the auxiliary normed space is with norm The other method is used if the disk is absorbing: in this case, the auxiliary normed space is the quotient space If the disk is both bounded and absorbing then the two auxiliary normed spaces are canonically isomorphic (as topological vector spaces and as normed spaces).
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In functional analysis, two me ...... spaces and as normed spaces).
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If is a disk in a topological ...... inclusion map is continuous.
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Let be a disk in a vector spa ...... t of then is a Banach space.
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Theorem
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Proof
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In functional analysis, two me ...... spaces and as normed spaces).
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Auxiliary normed space
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