Nous considérons des opérateurs linéaires bornés définis sur des espaces normés réels, et dont les images sont dans des espaces quaternioniques. Nous étudions les normes des extensions quaternioniques de ces opérateurs.
We consider bounded linear operators defined on real normed spaces, and with range in quaternionic spaces. We study the norms of the quaternionic extensions of such operators.
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@article{CRMATH_2005__340_9_639_0,
author = {Alpay, Daniel and Luna-Elizarrar\'as, Maria-Elena and Shapiro, Michael},
title = {Normes des extensions quaternionique d'op\'erateurs r\'eels},
journal = {Comptes Rendus. Math\'ematique},
pages = {639--643},
publisher = {Elsevier},
volume = {340},
number = {9},
year = {2005},
doi = {10.1016/j.crma.2005.03.030},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.03.030/}
}
TY - JOUR AU - Alpay, Daniel AU - Luna-Elizarrarás, Maria-Elena AU - Shapiro, Michael TI - Normes des extensions quaternionique d'opérateurs réels JO - Comptes Rendus. Mathématique PY - 2005 SP - 639 EP - 643 VL - 340 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.03.030/ DO - 10.1016/j.crma.2005.03.030 LA - fr ID - CRMATH_2005__340_9_639_0 ER -
%0 Journal Article %A Alpay, Daniel %A Luna-Elizarrarás, Maria-Elena %A Shapiro, Michael %T Normes des extensions quaternionique d'opérateurs réels %J Comptes Rendus. Mathématique %D 2005 %P 639-643 %V 340 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.03.030/ %R 10.1016/j.crma.2005.03.030 %G fr %F CRMATH_2005__340_9_639_0
Alpay, Daniel; Luna-Elizarrarás, Maria-Elena; Shapiro, Michael. Normes des extensions quaternionique d'opérateurs réels. Comptes Rendus. Mathématique, Tome 340 (2005) no. 9, pp. 639-643. doi : 10.1016/j.crma.2005.03.030. http://www.numdam.org/articles/10.1016/j.crma.2005.03.030/
[1] Quaternionic quantum mechanics and non commutative dynamics (available at) | arXiv
[2] Quaternionic Quantum Mechanics and Quantum Fields, Internat. Ser. Monographs Phys., vol. 88, Clarendon Press, Oxford University Press, New York, 1995
[3] Reproducing kernel quaternionic Pontryagin spaces, Integral Equations Operator Theory, Volume 50 (2004), pp. 431-476
[4] Espaces vectoriels topologiques. Chapitres 1 à 5, Masson, Paris, 1981 (Éléments de mathématique [Elements of mathematics])
[5] Operator Spaces, London Math. Soc. Monographs, vol. 23, 2000
[6] Finite-Dimensional Linear Analysis: A Systematic Presentation in Problem Form, MIT Press, Cambridge, 1974
[7] Résumé des résultats essentiels dans la théorie des produits tensoriels topologiques et des espaces nucléaires, Ann. Inst. Fourier (Grenoble), Volume 4 (1954), pp. 73-112 (1952)
[8] Concerning the Hahn–Banach theorem, Proc. Amer. Math. Soc., Volume 50 (1975), pp. 322-327
[9] Self-adjoint operators and pairs of Hermitian forms over the quaternions, Linear Algebra Appl., Volume 299 (1999) no. 1–3, pp. 101-117
[10] M.E. Luna-Elizarrarás, M. Shapiro, On some properties of quaternionic inner product spaces, Proceedings of the Twenty-Fifth International Colloquium on Group Theoretical Methods in Physics, in press
[11] M.E. Luna-Elizarrarás, M. Shapiro, Preservation of the norms of linear operators acting on some quaternionic function spaces, Oper. Theory: Adv. Appl., in press
[12] Analytic Functionals on the Sphere, Transl. Math. Monographs, vol. 178, American Mathematical Society, 1998
[13] Sur les maxima des formes bilinéaires et sur les fonctionelles linéaires, Acta Math., Volume 49 (1926), pp. 465-497
[14] Complex structure on a real Hilbert space and symplectic structure on a complex Hilbert space, J. Math. Phys., Volume 29 (1988), pp. 1069-1078
[15] Spectral theory for unitary operators on a quaternionic Hilbert space, J. Math. Phys., Volume 28 (1987), pp. 1941-1946
[16] Über Fortsetzung von linearen Funktionalen in linearen komplexen Räumen und linearen Quaternionräumen, Mat. Sb. (N.S.), Volume 3 (1938), pp. 353-358
[17] Convexity theorems generalizing those of M. Riesz and Hadamard with some applications, Comm. Sem. Math. Univ. Lund = Medd. Lunds Univ. Sem., Volume 9 (1948), pp. 1-58
[18] Some relations between the norm of an operator and that of its complex extension, Mat. Issled., Volume 42 (1976), pp. 3-12
[19] Normal operators on quaternionic Hilbert spaces, Trans. Amer. Math. Soc., Volume 162 (1971), pp. 337-350
[20] Quaternions and matrices of quaternions, Linear Algebra Appl., Volume 251 (1997), pp. 21-57
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