On a certain class of always convergent sequences and the Rayleigh quotient iterations. (English) Zbl 0726.47001

The author uses the convergence \[ \int | f|^{n+1}d\mu /\int | f|^ nd\mu \to \| f\|_{L_{\infty}},\quad f\in L_{\infty}, \] to approximate the spectral radius r(T) of a linear continuous operator on a complex Hilbert space H, T: \(H\to H\), \(T^*T=TT^*\), by \[ \| Tx_ n\| /\| x_ n\| \to r(T),\quad x_{n+1}=Tx_ n,\quad x_ 0\not\in Ker T. \]
Reviewer: G.Bruckner


47A10 Spectrum, resolvent
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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