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∈ℕ ∈ E.

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DOI

10.3103/s1055134417040022

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