Angle preserving transformations of Hilbert bundles

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

9:00-10:00,April 11,2023   A503

Abstract:

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 = αJ for a bounded, strictly positive and continuous scalar function α on X and a module into isometry J : H → K. When A is noncommutative, we discuss those transformations preserving orthogonality and parallelism.

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