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

MSC:

 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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References:

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