Research on complex symmetric operators and C-normal operators

The study of complex symmetric operators and \boldsymbolC\text- normal operators has flourished in operator theory that has sparked the interest of many scholars. It is closely related to matrix theory, function space operator theory, and quantum mechanics, and has important theoretical and practical significance. In this paper, we introduce the properties of complex symmetric operators and \boldsymbolC\text- normal operators, and give a new method to prove the refined polar decomposition theorem of complex symmetric operators and \boldsymbolC\text- normal operators based on the block operator technique. The sufficient conditions for \boldsymbolC\text- normal operators to complex symmetric operators are also studied.