Abstract
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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Acknowledgements
The authors are grateful to anonymous referee for helpful comments and suggestions which helped to improve the presentation of the results in the article. This work is supported in part by the Shandong Provincial Natural Science Foundation #ZR2019MA065.
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Communicated by Daniel Aron Alpay.
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Jiang, B., Tian, Y. Universal Decomposition Equalities for Operator Matrices in a Hilbert Space. Complex Anal. Oper. Theory 14, 70 (2020). https://doi.org/10.1007/s11785-020-01029-8
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DOI: https://doi.org/10.1007/s11785-020-01029-8