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Isometries and Hermitian operators on complex symmetric sequence spaces

Abstract

We consider a complex symmetric sequence space E that possesses the Fatou property and is different from l2. We prove that, for every surjective linear isometry V on E, there exist λ n ∈ ℂ with |λ n | = 1 and a bijective mapping π on the set ℕ of natural numbers such that

$$V\left( {\left\{ {\xi _n } \right\}_{n \in \mathbb{N}} } \right) = \left\{ {\lambda _n \xi _{\pi (n)} } \right\}_{n \in \mathbb{N}}$$

for every {ξ n {n∈ℕE.

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Correspondence to B. R. Aminov.

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Original Russian Text © B.R. Aminov and V.I. Chilin, 2017, published in Matematicheskie Trudy, 2017, Vol. 20, No. 1, pp. 21–42.

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Aminov, B.R., Chilin, V.I. Isometries and Hermitian operators on complex symmetric sequence spaces. Sib. Adv. Math. 27, 239–252 (2017). https://doi.org/10.3103/S1055134417040022

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Keywords

  • surjective isometry
  • complex symmetric space
  • Fatou property