Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II

Dodzi Attimu; Toka Diagana

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 3, page 431-442
  • ISSN: 0010-2628

Abstract

top
The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space 𝔼 ω × 𝔼 ω by linear operators. More precisely, upon making some suitable assumptions we prove that if ϕ is a non-degenerate bilinear form on 𝔼 ω × 𝔼 ω , then ϕ is representable by a unique linear operator A whose adjoint operator A * exists.

How to cite

top

Attimu, Dodzi, and Diagana, Toka. "Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II." Commentationes Mathematicae Universitatis Carolinae 48.3 (2007): 431-442. <http://eudml.org/doc/250222>.

@article{Attimu2007,
abstract = {The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space $\mathbb \{E\}_\omega \times \mathbb \{E\}_\omega $ by linear operators. More precisely, upon making some suitable assumptions we prove that if $\varphi $ is a non-degenerate bilinear form on $\mathbb \{E\}_\omega \times \mathbb \{E\}_\omega $, then $\varphi $ is representable by a unique linear operator $A$ whose adjoint operator $A^*$ exists.},
author = {Attimu, Dodzi, Diagana, Toka},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {non-Archimedean Hilbert space; bilinear form; continuous linear functionals; non-Archimedean Riesz theorem; bounded bilinear form; stable unbounded bilinear form; unstable unbounded bilinear form; non-Archimedean Hilbert space; bilinear form; continuous linear functionals; non-Archimedean Riesz theorem},
language = {eng},
number = {3},
pages = {431-442},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II},
url = {http://eudml.org/doc/250222},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Attimu, Dodzi
AU - Diagana, Toka
TI - Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 3
SP - 431
EP - 442
AB - The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space $\mathbb {E}_\omega \times \mathbb {E}_\omega $ by linear operators. More precisely, upon making some suitable assumptions we prove that if $\varphi $ is a non-degenerate bilinear form on $\mathbb {E}_\omega \times \mathbb {E}_\omega $, then $\varphi $ is representable by a unique linear operator $A$ whose adjoint operator $A^*$ exists.
LA - eng
KW - non-Archimedean Hilbert space; bilinear form; continuous linear functionals; non-Archimedean Riesz theorem; bounded bilinear form; stable unbounded bilinear form; unstable unbounded bilinear form; non-Archimedean Hilbert space; bilinear form; continuous linear functionals; non-Archimedean Riesz theorem
UR - http://eudml.org/doc/250222
ER -

References

top
  1. Basu S., Diagana T., Ramaroson F., A p -adic version of Hilbert-Schmidt operators and applications, J. Anal. Appl. 2 (2004), 3 173-188. (2004) Zbl1077.47061MR2092641
  2. de Bivar-Weinholtz A., Lapidus M.L., Product formula for resolvents of normal operator and the modified Feynman integral, Proc. Amer. Math. Soc. 110 (1990), 2 449-460. (1990) MR1013964
  3. Diagana T., Representation of bilinear forms in non-Archimedean Hilbert space by linear operators, Comment. Math. Univ. Carolin. 47 (2006), 4 695-705. (2006) Zbl1150.47408MR2337423
  4. Diagana T., Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications, Ann. Math. Blaise Pascal 12 (2005), 1 205-222. (2005) Zbl1087.47061MR2126449
  5. Diagana T., Erratum to: “Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications", Ann. Math. Blaise Pascal 13 (2006), 105-106. (2006) MR2233015
  6. Diagana T., Bilinear forms on non-Archimedean Hilbert spaces, preprint, 2005. 
  7. Diagana T., Fractional powers of the algebraic sum of normal operators, Proc. Amer. Math. Soc. 134 (2006), 6 1777-1782. (2006) Zbl1092.47027MR2207493
  8. Diagana T., An Introduction to Classical and p -adic Theory of Linear Operators and Applications, Nova Science Publishers, New York, 2006. Zbl1118.47323MR2269328
  9. Diarra B., An operator on some ultrametric Hilbert spaces, J. Analysis 6 (1998), 55-74. (1998) Zbl0930.47049MR1671148
  10. Diarra B., Geometry of the p -adic Hilbert spaces, preprint, 1999. 
  11. Johnson G.W., Lapidus M.L., The Feynman Integral and Feynman Operational Calculus, Oxford Univ. Press, Oxford, 2000. MR1771173
  12. Kato T., Perturbation Theory for Linear Operators, Springer, New York, 1966. Zbl0836.47009MR0203473
  13. Ochsenius H., Schikhof W.H., Banach Spaces Over Fields with an Infinite Rank Valuation, p -adic Functional Analysis, (Poznan, 1998), Marcel Dekker, New York, 1999, pp.233-293. MR1703500
  14. van Rooij A.C.M., Non-Archimedean Functional Analysis, Marcel Dekker, New York, 1978. Zbl0396.46061MR0512894

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.