Banach spaces which satisfy linear identities

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Abstract

In 1935, Jordan and von Neumann proved that any Banach space which satisfies the parallelogram law ‖x + y‖2 + ‖x - y‖2 = 2(‖x‖2 + ‖y‖2) for all elements x and y must be a Hubert space. Subsequent authors have found norm conditions weaker than (1) which require a Banach space to be a Hubert space. Notable examples include the results of Day, Lorch, Senechalle and Carlsson. In this paper, we study nontrivial linear identities such as (Formula Presented) for all elements xi on a Banach space X.

Original languageEnglish (US)
Pages (from-to)221-234
Number of pages14
JournalPacific Journal of Mathematics
Volume74
Issue number1
DOIs
StatePublished - Jan 1978
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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