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Some equivalent metrics for bounded normal operators

Mohammad Reza Jabbarzadeh; Rana Hajipouri — 2018

Mathematica Bohemica

Some stronger and equivalent metrics are defined on $ℳ$ , the set of all bounded normal operators on a Hilbert space $H$ and then some topological properties of $ℳ$ are investigated.

Centered weighted composition operators via measure theory

Mohammad Reza Jabbarzadeh; Mehri Jafari Bakhshkandi — 2018

Mathematica Bohemica

We describe the centered weighted composition operators on $L^{2} (Σ)$ in terms of their defining symbols. Our characterizations extend Embry-Wardrop-Lambert’s theorem on centered composition operators.

Weighted Frobenius-Perron operators and their spectra

Mohammad Reza Jabbarzadeh; Rana Hajipouri — 2017

Mathematica Bohemica

First, some classic properties of a weighted Frobenius-Perron operator $𝒫_{ϕ}^{u}$ on $L^{1} (Σ)$ as a predual of weighted Koopman operator $W = u U_{ϕ}$ on $L^{\infty} (Σ)$ will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of $𝒫_{ϕ}^{u}$ under certain conditions.

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