Complex Symmetric Operators And Related Topics

In linear algebra, there is a lot of work on the theory of symmetric matrices, whichhave many motivations in function theory, matrix analysis and other mathematicaldisciplines. Generalizing the notion of complex symmetric matrices, Garcia and Putinarinitiated the study of complex symmetric operators on Hilbert spaces. Some importantresults concerning the internal structure of complex symmetric operators have beenobtained.We always denote by H a complex separable Hilbert space and by B (H) the algebraof all bounded linear operators on H.Defnition1A conjugation on H is a conjugate-linear map: H→H satisfyingthat C~2=I and...