Some generalizations of Kadison's theorem: a survey

摘要: Let H be a complex Hilbert space and let K(H) L(H) denote respectively the of compact bounded linear operators on H. A well known result Kadison [16] (see also Chapter 6 [9]) describes surjective isometries these spaces as T → UTV or UT trV , where U V are unitaries tr denotes Banach adjoint an operator via identification with H∗. For general X Y in this article we will consider various interpretations above order to completely describe K(X, ) L(X,Y ). Clearly for ∈ L(X) L(Y ), is isometry leaving compacts invariant. Such shall call standard isometries. Note that if : ∗ X∗ then ∗U L(X, We assume throughout note not isometric . This hypothesis missing from statement theorems [18] [33] In need form examples below). focus only following three variations Kadison’s theorem. recall bidual under canonical embedding bi-transpose K(H). And thus any onto 1. When describable form?