Hong-Ke Du

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Let P and Q be two idempotents on a Hilbert space. In 2005, J. Giol in [Segments of bounded linear idempotents on a Hilbert space, J. Funct. Anal. 229(2005) 405-423] had established that, if P + Q − I is invertible, then P and Q are homotopic with˜s(P, Q) ≤ 2. In this paper, we have given a necessary and sufficient condition that˜s(P, Q) ≤ 2, where˜s(P, Q)(More)
Let P, Q be two linear idempotents on a Banach space. We show that the closeness of the range and complementarity of the kernel (range) of linear combinations of P and Q are independent of the choice of coefficients. This generalizes known results and shows that many spectral properties do not depend on the coefficients. The non-singularity of the(More)
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