Abstract
A theorem of J.R.Partington on the resolvent of hermitian operators ([11], Th.5) is extended to a wider class of operators and a related problem on the growth of subharmonic functions is discussed.
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References
Beurling, A., Analytic continuation across a linear boundary. Acta Math. 128 (1972), 153 – 162.
Ciorănescu, I., Duality Mappings in the Non — Linear Functional Analysis (in Rumanian). Editura Academici, Bucuresti 1974; English review, MR 52 4038.
Ciorănescu, I. — Zsidó, L. , ω-Ultradistri but ions and the i r application to operatortheory. Spectral Theory (Banach Center Pul1ications, Vol.8), Polish Scientific Publishers, Warsaw 1982, 77 – 220.
Colojoară, I. — Foias, C, Theory of Generalized Spectral Operators . Gordon and Breach, New York / London / Paris 1968.
Domar, Y., On the existence of a largest subharmonic nainorant of a given function. Arkiv for Mat. 3 (1958) , 429–440.
Dyn’kin, E.M., Functions with given estimate for ∂f / ∂z and N. Levinson’s theorem (in Russian). Mat. Sbornik 89(131) (1972), 182–190; English transl. in Math. USSR Sbornik 18 (1972), 181–189.
Gurariĭ, V.P., On Levinson’s theorem concerning families of analytic fuctions (in Russian). Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 19 (1970), 215–220; English transl. in Sem. Math. Inst. Teningrad 19 (1972), 124 – 127.
Hayman, W.K. — Kennedy, P.B., Subharmonic Functions, Vol. 1. Academic Press, London / New York / San Francisco 1976.
Lumer, G. -Phillips, R.S., Dissipative Operators in a Banach Space. Pacific J. Math. 11. (1961), 679 – 698.
Markus, A.S., Some criteria for the completeness of a system of root vectors of a linear operator in a Banach space (in Russian). Math. Sbornik 70 (112) (1966), 526–561; English transl. in Amer. Math. Soc. Transl . (2) 85 (1969), 51–91.
Partington, J.R., The resolvent of a Hermitian operator on a Banach space. J.Tondon Math. Soc. (2) 27 (1983), 507
Radó, T., Subharmonic Functions. Springer — Verlag, Berlin 1937.
Stampfli, J.G. -Williams, J.P., Growth conditions and the numerical range in a Banach algebra. Tohoku Math. J. 20 (1968), 417 – 424.
Tillmann, H.G., Eine Erweiterung des Funktionalkalküls für 1ineare Operatoren. Math. Ann. 151 (1963), 424–430.
Wolf, F., On majorants of subharmonic and analytic functions. Bull. Amer. Math. Soc. 48 (1942), 925–932.
Zsidó, L., Invariant subspaces of compact perturbations of linear operators in Banach spaces. J. Operator Theory 1 (1979), 225 – 260.
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Zsidó, L. (1984). The Resolvent of Generalized Self-Adjoint Operators and a Related Growth Problem. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_8
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DOI: https://doi.org/10.1007/978-3-0348-5432-0_8
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