Universal Decomposition Equalities for Operator Matrices in a Hilbert Space
COMPLEX ANALYSIS AND OPERATOR THEORY(2020)
摘要
This paper establishes some universal decomposition equalities for operator matrices in a Hilbert space. It includes two basic universal operator matrix decompositions for two-by-two and four-by-four operator matrices, and two four-by-four universal operator matrix decompositions for a four-term linear combination x_0I + x_1P + x_2Q + x_3PQ , where P and Q are two commutative involutory or two commutative idempotent operators, and x_0, x_1, x_2, x_3 are four complex scalars. Many consequences are also presented concerning disjoint decomposition equalities, inverses, generalized inverses, collections of involutory, idempotent and tripotent operators generated from these linear combinations, etc.
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关键词
Hilbert space,Involutory operator,Idempotent operator,Linear combination,Decomposition,47A05,47A08,47A68
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