Abstract
Let \(\mathcal{B}(\mathcal{H})\) be the algebra of all bounded linear operators on a separable complex Hilbert space \(\mathcal{H}\). We introduce the J-decomposition property for projections in \(\mathcal{B}(\mathcal{H})\), and prove that the projection E in \(\mathcal{B}(\mathcal{H})\) has J-decomposition property with respect to a particular space decomposition, which is related to Hal-mos’ two projections theory. Using this, we characterize symmetries J such that the projection E is a J-projection (or J-positive projection, or J-negative projection). Also, we give the explicit representations of the maximum and the minimum of symmetries J such that the projection E is J-positive (or J-negative).
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The first named author was supported by NSF of China (No. 11601339) and the Natural Science Foundation of Jiangsu Province of China (No. BK20171421).
The second named author was supported by NSF of China (Nos. 11671242, 11571211) and the Fundamental Research Funds for the Central Universities (No. GK201801011).
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Xu, XM., Li, Y. Symmetries for J-projection. Anal Math 46, 393–407 (2020). https://doi.org/10.1007/s10476-020-0033-y
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DOI: https://doi.org/10.1007/s10476-020-0033-y