FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 6, PAGES 175-192

Elementary rotations of operators in regular Banach spaces

D. L. Tyshkevich

Abstract

View as HTML     View as gif image

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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k066/k06611h.htm
Last modified: February 26, 2007