FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

D. L. Tyshkevich

Abstract

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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.

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