Abstract
The classical Riesz-Dunford operator calculus (see, e.g., [1]) defines f (T) only for functions analytic in a neighborhood of the spectrum & (T) of the operator T. For operators with a unitary spectrum another familiar example is the calculus of Wermer [2].
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Literature Cited
Dunford, N., and Schwartz, J. T., Linear Operators, Vol. 1: General Theory, Interscience, New York (1958).
Wermer, J., The existence of invariant subspaces, Duke Math. J., 19 (4): 615 - 622 (1952).
Lyubich, Yu. I., and Matsaev, V. I., On operators with a divisible spectrum, Matem. Sborn., 56(98) (4): 533 - 468 (1962).
Levinson, N., Gap and Density Theorems (AMS Colloquium Publications, No. 26), American Mathematical Society, Providence, R. L (1940).
Gurarii, V. P. On Levinsons theorem concerning normal families of analytic functions, this volume, p. 124,
Domar, Y., On the existence of a largest subharmonic minorant of a given function, Arkiv Mat., 3 (5): 429 - 440 (1958).
Maeda, F., Generalized unitary operators, Bull. Amer. Math. Soc., 74 (4): 631 - 633 (1965).
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Dyn’kin, E.M. (1972). An Operator Calculus Based on The Cauchy—Green Formula, and the Quasi Analyticity of the Classes D(h). In: Nikol’skii, N.K. (eds) Investigations in Linear Operators and Function Theory. Seminars in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1526-2_9
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DOI: https://doi.org/10.1007/978-1-4757-1526-2_9
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