Abstract
We generalize the well-known Sinclair lemma for Hermitian elements, proving pointwise versions for generalized scalar operators and unbounded skew-Hermitian operators.
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E. Albrecht,On some classes of generalized spectral operators, Arch. Math.,30 (1978), 297–303.
C. Apostol,Sur l’équivalence asymptotique des opérateurs, Rev. Roumaine Math. Pures Appl.12 (1967), 601–607.
C. J. K. Batty,Dissipative mappings and well-behaved derivations, J. London Math. Soc. (2)18 (1978), 527–533.
R. P. Boas, Jr.,Entire Functions, Academic Press, New York, 1954.
F. F. Bonsall and J. Duncan,Numerical Ranges of Operators, Parts I and II, London Math. Soc. Lecture Notes 2 and 10, Cambridge, 1971 and 1973.
O. Bratteli and D. W. Robinson,Unbounded derivations of C*-algebras II, Commun. Math. Phys.46 (1976), 11–30.
A. Browder,On Bernstein’s inequality and the norm of Hermitian operators, Amer. Math. Monthly78 (1971), 871–873.
P. R. Chernoff,Optimal Landau-Kolmogorov inequalities for dissipative operators in Hilbert and Banach spaces, Adv. in Math.34 (1979), 137–144.
K. Clancey,Seminormal Operators, Lecture Notes in Math. 742, Springer-Verlag, 1979.
I. Colojoara and C. Foias,Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
M. J. Crabb and P. G. Spain,Commutators and normal operators, Glasgow Math. J.18 (1977), 197–198.
N. Dunford and J. T. Schwartz,Linear Operators, Part I, Interscience Publishers, New York, 1958.
T. Furuta,On the class of paranormal operators, Proc. Japan Acad. Ser. A, Math. Sci.43 (1967), 594–598.
V. I. Istratescu,Introduction to Linear Operator Theory, Marcel Dekker Inc., New York, 1981.
V. E. Katznelson,The norm of a conservative operator equals its spectral radius, Mat. Issled.5 (1970), No. 3, 186–189 (in Russian).
A. N. Kolmogorov,On inequalities between the upper bounds of the successive derivatives of an arbitrary function on an infinite interval, Uchen. Zap. Moskov. Gos. Univ. Mat.30 (1939), No. 3, 3–16; Amer. Math. Soc. Transl. (1), No. 4 (1949), 1–19 and No. 2 (1962), 233–243.
B. Ja. Levin,Distribution of Zeros of Entire Functions, GITTL, Moscow, 1956; English transl., Amer. Math. Soc., Providence, R. I., 1964.
G. Lumer and R. S. Phillips,Dissipative operators in a Banach space, Pacific J. Math.11 (1961), 679–698.
J. R. Partington,The resolvent of a Hermitian operator on a Banach space, J. London Math. Soc. (2)27 (1983), 507–512.
I. J. Schoenberg and A. Cavaretta,Solution of Landau’s problem concerning higher derivatives on the halfline, University of Wisconsin MRC Report No. 1050, March 1970. Also in Proc. Conf. Constructive Function Theory — Varna 1970, Sofia, 1972.
A. M. Sinclair,The norm of a Hermitian element in a Banach algebra, Proc. Amer. Math. Soc.28 (1971), 446–450.
S. B. Stechkin,On inequalities between the upper bounds of the derivatives of an arbitrary function on the halfline, Mat. Zametki1 (1967), No. 6, 665–673. (Amer. Math. Soc. Transl. as Math. Notes.)
D. V. Widder,The Laplace Transform, Princeton, 1946.
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Boyadzhiev, K.N. Sinclair type inequalities for the local spectral radius and related topics. Israel J. Math. 57, 272–284 (1987). https://doi.org/10.1007/BF02766214
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DOI: https://doi.org/10.1007/BF02766214