MAPS PRESERVING m- ISOMETRIES ON HILBERT SPACE

被引：1

作者：

Majidi, Alireza ^{[1
]}

机构：

[1] Islamic Azad Univ, Mashhad Branch, Dept Math, Mashhad, Razavi Khorasan, Iran

来源：

KOREAN JOURNAL OF MATHEMATICS | 2019年 / 27卷 / 03期

关键词：

C*-algebra; Hilbert space; m-isometry; preserving linear map;

D O I：

10.11568/kjm.2019.27.3.735

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H be a complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we prove that if phi : B(H) -> B(H) is a unital surjective bounded linear map, which preserves m- isometrics m = 1, 2 in both directions, then there are unitary operators U, V is an element of B(H) such that phi(T) = UTV or phi(T) = (UTV)-V-tr for all T is an element of B(H), where T-tr is the transpose of T with respect to an arbitrary but fixed orthonormal basis of H.

引用

页码：735 / 741

页数：7

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