Path Connectivity of Idempotents on a Hilbert Space
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چکیده
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 s̃(P,Q) ≤ 2. In this paper, we have given a necessary and sufficient condition that s̃(P,Q) ≤ 2, where s̃(P,Q) denotes the minimal number of segments required to connect not only from P to Q, but also from Q to P in the set of idempotents.
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تاریخ انتشار 2008