Angle preserving transformations of Hilbert bundles

Ngai-Ching Wong   (National Sun Yat-sen University)

9:00-10:00,April 11,2023   A503


Let x,y be two vectors in a (real or complex) Hilbert C*- module H over a C*- algebra A. The angle (x,y) between x and y can be defined in several ways. When A = C_0(X) is a commutative C*- algebra, in other words, H is a continuous field of Hilbert spaces over a locally compact space X, we define the cosine of the angle, u = cos(x,y) C(X) , by the equation |hx,yi| = |x||y|u . We show that if T: H K is a linear module map between two Hilbert C_0(X)-modules preserving (cosines of) non-flat angles, then T = J for a bounded, strictly positive and continuous scalar function on X and a module into isometry J : H K. When A is noncommutative, we discuss those transformations preserving orthogonality and parallelism.

About the speaker: