$C^\ast$-algebras of operators in non-archimedean Hilbert spaces
Alvarez, J. Antonio
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 573-580 / Harvested from Czech Digital Mathematics Library
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We show several examples of n.a\. valued fields with involution. Then, by means of a field of this kind, we introduce ``n.a\. Hilbert spaces'' in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed.

Publié le : 1992-01-01
Classification:  46C05,  46L05,  46S10,  47S10 
@article{118527,
     author = {J. Antonio Alvarez},
     title = {$C^\ast$-algebras of operators in non-archimedean Hilbert spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {573-580},
     zbl = {0784.46063},
     mrnumber = {1240177},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118527}
}

Alvarez, J. Antonio. $C^\ast$-algebras of operators in non-archimedean Hilbert spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 573-580. http://gdmltest.u-ga.fr/item/118527/

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