Spectrum (linear operator)

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A bounded, linear operator O that maps a Banach space into itself has a spectrum of values {λ} provided there are non-zero vectors x_λ in the space such that O x_λ = λ x_λ. The {λ} are called characteristic values of O and {x_λ} the eigenvectors of O. The spectrum may consist of discrete values, a continuum of values, or a combination of both.^[1]

References[edit]

↑ A. N. Kolmogorov, Sergeĭ Vasilʹevich Fomin, S. V. Fomin (1999). “§30 Spectrum of an operator. Resolvents”, Elements of the Theory of Functions and Functional Analysis, Volume 1, Reprint of Graylock Press 1957 ed. Courier Dover Publications, pp. 110 ff. ISBN 0486406830.

[Fomin-1] A. N. Kolmogorov, Sergeĭ Vasilʹevich Fomin, S. V. Fomin (1999). “§30 Spectrum of an operator. Resolvents”, Elements of the Theory of Functions and Functional Analysis, Volume 1, Reprint of Graylock Press 1957 ed. Courier Dover Publications, pp. 110 ff. ISBN 0486406830.

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