The unitary group preserving maps (the infinite dimensional case)

Linear Maps on Factors which Preserve the Extreme Points of the Unit Ball

“…As a consequence of this result we immediately have the structure of surjective linear selfmaps of B(H ) which preserve the extreme points of the unit ball. In fact, Corollary 1 below is a significant generalization of a result of Rais [Rai,Lemma 3…”

“…The finite dimensional case of this problem was treated in [Mar], while the one on B(H ) (the algebra of all bounded linear operators acting on the Hilbert space H ) and on a general C Ł -algebra were solved in [Rai] and in [RuDy], respectively. In [Rai,Section 4] the problem of characterizing those linear maps on B(H ) which preserve the extreme points of the unit ball of B(H ) was implicitly raised and concerning bijective linear selfmaps of B(H ) which preserve the extreme points in question in both directions (i.e. the maps as well as their inverses are supposed to preserve the set of those extreme points) the author obtained a complete description.…”

Linear maps preserving G-quasi-isometry operators

“…By a linear preserver, we mean a linear map of an algebra A into itself which, roughly speaking, preserves certain properties of some elements on A. The problem has attracted the attention of many mathematicians in the last few decades (see, for instance, [3][4][5][6]8,11,13,14,[18][19][20][21]). In this paper, B(H) is the algebra of all bounded linear operators on a complex Hilbert space H. We should point out that a great deal of work has been devoted to the case when H is finite dimensional; that is, the case when B(H) is a matrix algebra (see survey articles [11,12,17]), and that the first papers concerning this case date back to the previous century [8].…”

Unitarily invariant Norms on Operators

“…By Theorem 3.6, L sends maximal isometries to maximal isometries. It follows from [9, Solution to Problem 107] (see also[20, Lemma 3]) that L is indeed an isometry of the spectral norm. Using the characterization [4, Corollary 3.3], we conclude that L is of the asserted form.…”