General explicit descriptions for intertwining operators and direct rotations of two orthogonal projections

In this paper, based on the block operator technique and operator spectral theory, general explicit descriptions for intertwining operators and direct rotations of two orthogonal projections are established. As a consequence, Kato's result (Kato, 1996 [14]) is improved, so are J. Avron, R. Seiler and B. Simon's Theorem 2.3 (Avron et al., 1994 [6]) and C. Davis, W.M. Kahan's result (Davis and Kahan, 1970 [11]).