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Garcia, M.C. and Palacios, A.R. (2014) Non-Associative Normed Algebras: Volume 1, The Vidav-Palmer and Gelfand-Naimark Theorems. Cambridge University Press.
https://doi.org/10.1017/9781107337817

has been cited by the following article:

• TITLE: Generalized Inverses in Jordan Algebras

  AUTHORS: Mustapha Laayouni

  KEYWORDS: Associative Algebra, Jordan Algebra, Generalized Inverse, Generalized Spectrum, Conorm

  JOURNAL NAME: Advances in Pure Mathematics, Vol.16 No.3, March 2, 2026

  ABSTRACT: The article introduces the concept of generalized inverses in Jordan algebras as an analog to the classical generalized inverses in the absence of the associativity. We define nonassociative generalized inverses based on quadartic operator U a , explore properties of these notion (e.g., existence, characterization, coincidence with the notion of generalized inverse when Jordan algebra is special or associative, compactness of the generalized spectrum introduced here), and prove results analogous to those in associative algebras, including a Jordan version of the generalized resolvent and a conorm.