| Title:
|
Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II (English) |
| Author:
|
Attimu, Dodzi |
| Author:
|
Diagana, Toka |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
431-442 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space $\Bbb E_\omega \times \Bbb E_\omega $ by linear operators. More precisely, upon making some suitable assumptions we prove that if $\varphi $ is a non-degenerate bilinear form on $\Bbb E_\omega \times \Bbb E_\omega $, then $\varphi $ is representable by a unique linear operator $A$ whose adjoint operator $A^*$ exists. (English) |
| Keyword:
|
non-Archimedean Hilbert space |
| Keyword:
|
bilinear form |
| Keyword:
|
continuous linear functionals |
| Keyword:
|
non-Archimedean Riesz theorem |
| Keyword:
|
bounded bilinear form |
| Keyword:
|
stable unbounded bilinear form |
| Keyword:
|
unstable unbounded bilinear form |
| MSC:
|
46S10 |
| MSC:
|
47A07 |
| MSC:
|
47S10 |
| idZBL:
|
Zbl 1199.47334 |
| idMR:
|
MR2374125 |
| . |
| Date available:
|
2009-05-05T17:03:56Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119670 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/119629 |
| . |
| Reference:
|
[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. Zbl 1077.47061, MR 2092641 |
| Reference:
|
[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. MR 1013964 |
| Reference:
|
[3] Diagana T.: Representation of bilinear forms in non-Archimedean Hilbert space by linear operators.Comment. Math. Univ. Carolin. 47 (2006), 4 695-705. Zbl 1150.47408, MR 2337423 |
| Reference:
|
[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. Zbl 1087.47061, MR 2126449 |
| Reference:
|
[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. MR 2233015 |
| Reference:
|
[6] Diagana T.: Bilinear forms on non-Archimedean Hilbert spaces.preprint, 2005. |
| Reference:
|
[7] Diagana T.: Fractional powers of the algebraic sum of normal operators.Proc. Amer. Math. Soc. 134 (2006), 6 1777-1782. Zbl 1092.47027, MR 2207493 |
| Reference:
|
[8] Diagana T.: An Introduction to Classical and $p$-adic Theory of Linear Operators and Applications.Nova Science Publishers, New York, 2006. Zbl 1118.47323, MR 2269328 |
| Reference:
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[9] Diarra B.: An operator on some ultrametric Hilbert spaces.J. Analysis 6 (1998), 55-74. Zbl 0930.47049, MR 1671148 |
| Reference:
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[10] Diarra B.: Geometry of the $p$-adic Hilbert spaces.preprint, 1999. |
| Reference:
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[11] Johnson G.W., Lapidus M.L.: The Feynman Integral and Feynman Operational Calculus.Oxford Univ. Press, Oxford, 2000. MR 1771173 |
| Reference:
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[12] Kato T.: Perturbation Theory for Linear Operators.Springer, New York, 1966. Zbl 0836.47009, MR 0203473 |
| Reference:
|
[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. MR 1703500 |
| Reference:
|
[14] van Rooij A.C.M.: Non-Archimedean Functional Analysis.Marcel Dekker, New York, 1978. Zbl 0396.46061, MR 0512894 |
| . |
