Weyl's theorem for complex symmetric operators
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DOI: 10.1016/j.jmaa.2019.02.031
Abstract: Abstract An operator on Hilbert space is complex symmetric if it can be represented as a symmetric matrix relative to some orthonormal basis of the space. It is proved in this paper that each complex… read more here.
Keywords: weyl theorem; theorem complex; symmetric operators; symmetric ... See more keywords
ON ∞-COMPLEX SYMMETRIC OPERATORS
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DOI: 10.1017/s0017089516000550
Abstract: Abstract In this paper, we study spectral properties and local spectral properties of ∞-complex symmetric operators T. In particular, we prove that if T is an ∞-complex symmetric operator, then T has the decomposition property… read more here.
Keywords: symmetric operators; complex symmetric;
Phillips symmetric operators and their extensions
Sign Up to like & getrecommendations! Published in 2018 at "Banach Journal of Mathematical Analysis"
DOI: 10.1215/17358787-2018-0009
Abstract: Let $S$ be a symmetric operator with equal defect numbers and let $\mathfrak{U}$ be a set of unitary operators in a Hilbert space $\mathfrak{H}$. The operator $S$ is called $\mathfrak{U}$-invariant if $US=SU$ for all $U\in\mathfrak{U}$.… read more here.
Keywords: symmetric operators; mathfrak invariant; symmetric operator; phillips symmetric ... See more keywords
Skew m-complex symmetric operators
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DOI: 10.2298/fil1910975c
Abstract: In this paper we study skew m-complex symmetric operators. In particular, we show that if T ? L(H) is a skew m-complex symmetric operator with a conjugation C, then eitT , e-itT , and e-itT*… read more here.
Keywords: operators skew; skew complex; symmetric operators; complex symmetric ... See more keywords
Extension of the notion of P-symmetric operators using the Aluthge transform I
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DOI: 10.2298/fil2416669e
Abstract: The class of ?P-symmetric operators is introduced. Certain properties of this class of operators are obtained. Among other things, it is shown that (1) This class includes the quasinormal operators, isometries, co-isometries, partial isometries with… read more here.
Keywords: symmetric; extension notion; notion symmetric; using aluthge ... See more keywords
Range inclusion and diagonalization of complex symmetric operators
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DOI: 10.4153/s0008414x24000294
Abstract: Abstract We consider the range inclusion and the diagonalization in the Jordan algebra $\mathcal {S}_C$ of C-symmetric operators, that are, bounded linear operators T satisfying $CTC =T^{*}$ , where C is a conjugation on a… read more here.
Keywords: inclusion diagonalization; operator; range inclusion; symmetric operators ... See more keywords