ABSTRACT
Let H be a separable infinite-dimensional complex Hilbert space and L(H) the Banach space of bounded linear operators onH with operator norm. As usual, we denote the inner product on H by 〈·, ·〉. Since L(H) is also a Banach algebra we can investigate the structure of the isometries of subalgebras or ideals of L(H). The isometries of L(H) are well known to be the product of a unitary and a Jordan∗-isomorphism as given by Kadison’s Theorem 6.1.1. The question arises as to whether or not the isometries of subalgebras have the same form as isometries of the full algebra. We have seen that this is not the case for the commutative version of L(H), namely C(K). We considered the form of isometries on certain types of subalgebras of C∗ algebras in Chapter 6. In this chapter we consider a more special case of this problem, namely the isometries of various minimal norm ideals of L(H).
