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Fourier series criteria for operator decomposability (1986)

Berkson, Earl ; Gillespie, T. A.

Springer

Integral equations and operator theory 9 (1986), S. 767-789

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ISSN: 1420-8989

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Let U be an invertible operator on a Banach space Y. U is said to betrigonometrically well-bounded provided the sequence {Un} n ∞ =−∞ is the Fourier-Stieltjes transform of a suitable projection-valued function E(·): [0, 2π]→ℬ(Y). This class of operators is known to apply naturally to a variety of classical phenomena which exclude the presence of spectral measures. In the case Y reflexive we use the Cesáro means σn(U, t) of the trigonometric series ∑k≠0 k−eiktUk, whichformally transfers the discrete Hilbert transform to Y, in order to give three separate necessary and sufficient conditions for U to be trigonometrically well-bounded. One of these conditions is sup {∥σn(U,t)∥: n ≥ 1, t ∈ [0,2π]} 〈 ∞

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01202516

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