广义幂等算子差的可逆性

Abstract

Abstract:

Let P and Q be two idempotents on a Hilbert space H. The set ω(P) of generalized idempotent operators with respect to P is defined by ω(P)={A ∈B(H): A²=α A+β P, AP=PA=A, P²=P, for some α, β ∈C}. In this note, the author proves that the invertibility of A-B is completely determined by the invertibility of P-Q, and R(AB) is closed if and only if R(PQ) is closed for arbitrary A ∈ω(P) and B ∈ω(Q) such that A²=α A + β P, B²=mB+nQ, where β n ≠ 0, α and m are arbitrary.

Key words: Idempotent, Invertibility, Operator matrix

CLC Number:

47A05

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DENG Chun-Yuan. Invertibility of Differences of Two Generalized |Idempotent Operators[J].Acta mathematica scientia,Series A, 2009, 29(6): 1477-1486.

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Invertibility of Differences of Two Generalized |Idempotent Operators

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