Geodesic
On skew (a, m)-symmetric operators in a Hilbert space
Filomat, Tome 36 (2022) no. 10, p. 3261

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DOI

In this paper, we study skew (A,m)-symmetric operators in a complex Hilbert spaceH . Firstly, by introducing the generalized notion of left invertibility we show that if T ∈ B(H) is skew (A,m)-symmetric, then eisT is left (A,m)-invertible for every s ∈ R. Moreover, we examine some conditions for skew (A,m)- symmetric operators to be skew (A,m − 1)-symmetric. The connection between c0-semigroups of (A,m)- isometries and skew (A,m)-symmetries is also described. Next, we investigate the stability of a skew (A,m)-symmetric operator under some perturbation by nilpotent operators commuting with T. In addition, we show that if T is a skew (A,m)-symmetric operator, then Tn is also skew (A,m)-symmetric for odd n. Finally, we consider a generalization of skew (A,m)-symmetric operators to the multivariable setting. We introduce the class of skew (A,m)-symmetric tuples of operators and characterize the joint approximate point spectrum of such a family.
DOI : 10.2298/FIL2210261R
Classification : 46C05, 47A10, 47A53, 47B20
Keywords: Skew (A, m)-symmetric operator, left (A, m)-invertible operator, (A, m)-Isometric operator, joint point spectrum, joint approximate point spectrum 
Rchid Rabaoui. On skew (a, m)-symmetric operators in a Hilbert space. Filomat, Tome 36 (2022) no. 10, p. 3261 . doi: 10.2298/FIL2210261R
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     author = {Rchid Rabaoui},
     title = {On skew (a, m)-symmetric operators in a {Hilbert} space},
     journal = {Filomat},
     pages = {3261 },
     year = {2022},
     volume = {36},
     number = {10},
     doi = {10.2298/FIL2210261R},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2210261R/}
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