Approximation of the polar factor of an operator acting on a Hilbert space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Mbekhta, Mostafa¹ 

[1] Univ Lille, Dept Math, CNRS, UMR 8524, F-59655 Villeneuve Dascq, France

关键词: Polar decomposition;    Polar factor;    Partial isometrics;    Approximations;   

DOI  :  10.1016/j.jmaa.2020.123954

来源: Elsevier

【 摘 要 】

Let H be a complex Hilbert space and let B(H) be the algebra of all bounded linear operators on H. The polar decomposition theorem asserts that every operator T is an element of B(H) can be written as the product T = VP of a partial isometry V is an element of B(H) and a positive operator P is an element of B(H) such that the kernels of V and P coincide. Then this decomposition is unique. V is called the polar factor of T. Moreover, we have automatically P = vertical bar T vertical bar = (T*T)(1/2). Unlike P, we do not have any representation formula for V. In this paper, we give several explicit formulas representing the polar factor. These formulas allow for methods of approximations of the polar factor of T. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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