Complex symmetric operators and applications II |
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Authors: | Stephan Ramon Garcia Mihai Putinar |
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Institution: | Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080 ; Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080 |
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Abstract: | A bounded linear operator on a complex Hilbert space is called complex symmetric if , where is a conjugation (an isometric, antilinear involution of ). We prove that , where is an auxiliary conjugation commuting with . We consider numerous examples, including the Poincaré-Neumann singular integral (bounded) operator and the Jordan model operator (compressed shift). The decomposition also extends to the class of unbounded -selfadjoint operators, originally introduced by Glazman. In this context, it provides a method for estimating the norms of the resolvents of certain unbounded operators. |
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Keywords: | Complex symmetric operator Takagi factorization inner function Aleksandrov-Clark operator Clark operator Aleksandrov measure compressed shift Jordan operator $J$-selfadjoint operator Sturm-Liouville problem |
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