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| The Jordan Algebra of Complex Symmetric Operators |
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Citation： |
Cun WANG,Sen ZHU.The Jordan Algebra of Complex Symmetric Operators[J].Chinese Annals of Mathematics B,2025,46(5):733~758 |
| Page view： 162
Net amount： 107 |
Authors： |
Cun WANG; Sen ZHU |
Foundation： |
the National Natural Science Foundation of China (Nos. 12401149,
12171195) and the National Key Research and Development Program of China (No. 2020YFA0714101). |
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| Abstract： |
For a conjugation C on a separable, complex Hilbert space H, the set SC of Csymmetric operators on H forms a weakly closed, selfadjoint, Jordan operator algebra. In
this paper, the authors study SC in comparison with the algebra B(H) of all bounded linear
operators on H, and obtain SC-analogues of some classical results concerning B(H). The
authors determine the Jordan ideals of SC and their dual spaces. Jordan automorphisms
of SC are classified. The authors determine the spectra of Jordan multiplication operators
on SC and their different parts. It is proved that those Jordan invertible ones constitute a
dense, path connected subset of SC. |
Keywords： |
Complex symmetric operator Jordan operator algebra Cartan factor Jordan ideal Automorphism |
Classification： |
47B99, 46L70, 17C65, 46K70 |
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