Perturbation theorems for Hermitian elements in Banach algebras
Studia Mathematica (1999)
- Volume: 134, Issue: 2, page 111-117
- ISSN: 0039-3223
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] B. Aupetit, A Primer on Spectral Theory, Springer, 1991.
- [2] B. Aupetit and D. Drissi Local spectrum and subharmonicity, Proc. Edinburgh Math. Soc. 39 (1996), 571-579. Zbl0861.47003
- [3] R. Bhatia, Matrix Analysis, Springer, 1997. Zbl0863.15001
- [4] R. Bhatia, C. Davis and P. Koosis, An extremal problem in Fourier analysis with applications to operator theory, J. Funct. Anal. 82 (1989), 138-150. Zbl0674.42002
- [5] R. Bhatia, C. Davis and A. McIntosh, Perturbation of spectral subspaces and solution of linear operator equations, Linear Algebra Appl. 52-53 (1983), 45-67. Zbl0518.47013
- [6] R. Bhatia and P. Rosenthal, How and why to solve the operator equation AX - XB = Y, Bull. London Math. Soc. 29 (1997), 1-21. Zbl0909.47011
- [7] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, Cambridge Univ. Press, 1971. Zbl0207.44802
- [8] A. Browder, On Bernstein's inequality and the norm of Hermitian operators, Amer. Math. Monthly 78 (1971), 871-873. Zbl0224.47011
- [9] D. E. Evans, On the spectrum of a one-parameter strongly continuous representation, Math. Scand. 39 (1976), 80-82. Zbl0356.47023
- [10] U. Haagerup and L. Zsidó, Resolvent estimate for Hermitian operators and a related minimal extrapolation problem, Acta Sci. Math. (Szeged) 59 (1994), 503-524. Zbl0821.47003
- [11] V. E. Katsnelson, A conservative operator has norm equal to its spectral radius, Mat. Issled. 5 (1970), 186-189 (in Russian). Zbl0226.47002
- [12] A. N. Kolmogorov, On inequalities between upper bounds of the successive derivatives of an arbitrary function on an infinite interval, Uchen. Zap. Moskov. Gos. Univ. Mat. 30 (1939), 3-16 (in Russian); English transl.: Amer. Math. Soc. Transl. 4 (1949), 233-243.
- [13] B. Ya. Levin, Lectures on Entire Functions, Transl. Math. Monographs 150, Amer. Math. Soc., 1996.
- [14] R. McEachin, A sharp estimate in an operator inequality, Proc. Amer. Math. Soc. 115 (1992), 161-165. Zbl0757.47014
- [15] J. R. Partington, The resolvent of a Hermitian operator on a Banach space, J. London Math. Soc. (2) 27 (1983), 507-512. Zbl0517.47003
- [16] A. M. Sinclair, The norm of a Hermitian element in a Banach algebra, Proc. Amer. Math. Soc. 28 (1971), 446-450. Zbl0242.46035
- [17] B. Sz.-Nagy, Über die Ungleichung von H. Bohr, Math. Nachr. 9 (1953), 255-259.
- [18] B. Sz.-Nagy and A. Strausz, On a theorem of H. Bohr, Mat. Termész. Értes. 57 (1938), 121-133 (in Hungarian).