Correct answer: (B) ‖T‖=1.; (C) T is self-adjoint.; (D) Range(T) is closed.
Explanation
Reflection Rx=(x_(−j)) is a self-adjoint isometry with R²=I. Thus T=(I+R)/2 is the orthogonal projection onto even sequences. Its nonzero projection norm is 1, it is self-adjoint and its range is closed. The even subspace is infinite-dimensional, so its projection is not compact: orthonormal even sequences remain separated. **B,C,D**.
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