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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:

[1] Bourbaki N.: Integrirovanie. Nauka, Moskva 1967. · Zbl 0156.06001
[2] Dunford N., Schwartz J. T.: Linejnye operatory I, II. Mir, Moskva 1962, 1966.
[3] Rudin W.: Principles of mathematical analysis. Mc Graw-Hill, Inc. New York 1964. · Zbl 0148.02903
[4] Rudin W.: Real and complex analysis. Mc Graw-Hill, Inc. New York I974. · Zbl 1038.00002
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