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Banach algebra

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Summary

An associative algebra over a normed field that is complete under a submultiplicative norm.

Record metadata

Carrier(s)

Data

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

complete normed algebra(construction junction)Banach algebra

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Require the shared norm and multiplication to satisfy abab\lVert ab \rVert \le \lVert a \rVert \lVert b \rVert.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Banach algebraBanach algebra + involution(construction junction)

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Supply the complete normed complex algebra structure on the same carrier and multiplication used by the star-algebra input.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources