-algebras of operators in non-archimedean Hilbert spaces

J. Antonio Alvarez

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 4, page 573-580
  • ISSN: 0010-2628

Abstract

top
We show several examples of n.av̇alued fields with involution. Then, by means of a field of this kind, we introduce “n.aḢilbert 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.

How to cite

top

Alvarez, J. Antonio. "$C^\ast $-algebras of operators in non-archimedean Hilbert spaces." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 573-580. <http://eudml.org/doc/247360>.

@article{Alvarez1992,
abstract = {We show several examples of n.av̇alued fields with involution. Then, by means of a field of this kind, we introduce “n.aḢilbert 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.},
author = {Alvarez, J. Antonio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {non-archimedean Hilbert space; non-archimedean $C^\ast $-algebra; non-Archimedean Hilbert space; non-Archimedean -algebra; n.a. Hilbert spaces; n.a. valued fields with involution; Hermitian sesquilinear form; algebra of bounded operators},
language = {eng},
number = {4},
pages = {573-580},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$C^\ast $-algebras of operators in non-archimedean Hilbert spaces},
url = {http://eudml.org/doc/247360},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Alvarez, J. Antonio
TI - $C^\ast $-algebras of operators in non-archimedean Hilbert spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 4
SP - 573
EP - 580
AB - We show several examples of n.av̇alued fields with involution. Then, by means of a field of this kind, we introduce “n.aḢilbert 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.
LA - eng
KW - non-archimedean Hilbert space; non-archimedean $C^\ast $-algebra; non-Archimedean Hilbert space; non-Archimedean -algebra; n.a. Hilbert spaces; n.a. valued fields with involution; Hermitian sesquilinear form; algebra of bounded operators
UR - http://eudml.org/doc/247360
ER -

References

top
  1. Alvarez García J.A., Involutions on non-archimedean fields and algebras, Actas XIII Jornadas Hispano-Lusas de Matemáticas, Valladolid, 1988, to appear. 
  2. Bayod Bayod J.M., Productos internos en espacios normados no arquimedianos, Doctoral dissertation, Universidad de Bilbao, 1976. 
  3. Keller H.A., Measures on orthomodular vector space lattices, Studia Mathematica 88 (1988), 183-195. (1988) Zbl0656.46051MR0931041
  4. Keller H.A., Measures on infinite-dimensional orthomodular spaces, Foundations of Physics 20 (1990), 575-604. (1990) MR1060623
  5. Monna A.F., Analyse non-Archimedienne, Springer-Verlag, 1970. Zbl0207.12402MR0295033
  6. Murphy G.J., Commutative non-archimedean -algebras, Pacific J. Math. 78 (1978), 433-446. (1978) Zbl0393.46054MR0519764
  7. Narici L., Beckenstein E., Bachman G., Functional Analysis and Valuation Theory, Marcel Dekker, 1971. Zbl0218.46004MR0361697
  8. Paschke W.L., Inner product modules over -algebras, Trans. Amer. Math. Soc. 182 (1973), 443-468. (1973) Zbl0239.46062MR0355613
  9. Rooij A.C.M. Van, Nonarchimedean Functional Analysis, Marcel Dekker, 1978. 

NotesEmbed ?

top

You must be logged in to post comments.