Elementary rotations of operators in regular Banach spaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 175-192
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In this paper we prove the existence of an elementary rotation (a Julia operator) for any continuous linear adjointable operator in a regular Banach space with inner product. The proof is based on a more general theorem of the same author about the existence of an elementary rotation for any linear operator in a category with quadratic splitting. This result is a generalization of a well-known result about the existence of an elementary rotation for any continuous linear operator in a Krein space. The result can be useful for constructing isometric and unitary dilations as well as characteristic functions of continuous linear operators acting in regular Banach spaces with inner product.
@article{FPM_2006_12_6_a10,
author = {D. L. Tyshkevich},
title = {Elementary rotations of operators in regular {Banach} spaces},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {175--192},
publisher = {mathdoc},
volume = {12},
number = {6},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a10/}
}
D. L. Tyshkevich. Elementary rotations of operators in regular Banach spaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 175-192. http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a10/