C*-Isomorphisms Associated with Two Projections on a Hilbert C*-Module

Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies C*-isomorphisms associated with projections introducing matched triple and semi-harmonious pair of projections. A (P, Q, H) is said be if H a Hilbert C*-module, P Q are on such that their infimum ∧ exists as an element $${\cal L}(H)$$ , where denotes set all adjointable operators H. The C*-subalgebras generated elements in {P − I} {P, denoted i(P, o(P, H), respectively. It proved each faithful representation (π, X) can induce $$(\tilde \pi ,X)$$ $$\matrix{{\tilde (P - \wedge Q) = (P) (Q),} \hfill \cr {\tilde (Q (Q) (Q).} } $$ When semi-harmonious, is, $$\overline {{\cal R}(P + Q)} R}(2I both orthogonally complemented H, it shown i(I I P, unitarily equivalent via unitary operator . counterexample constructed, which shows same may not true when fails semi-harmonious. Likewise, constructed whereas Some additional examples indicating new phenomena acting C*-modules also provided.