Some spectral inequalities involving generalized scalar operators

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1. [1] G. R. Allan and T. J. Ransford, Power-dominated elements in a Banach algebra, Studia Math. 94 (1989), 63-79. Zbl0705.46021
2. [2] C. Apostol, Teorie spectrală şi calcul functional, Stud. Cerc. Mat. 20 (1968), 635-668. 
3. [3] B. Aupetit, A Primer on Spectral Theory, Springer, 1991. 
4. [4] B. Aupetit and D. Drissi, Local spectrum theory revisited, to appear. 
5. [5] B. A. Barnes, Operators which satisfy polynomial growth conditions, Pacific J. Math. 138 (1987), 209-219. Zbl0693.47001
6. [6] R. G. Bartle and C. A. Kariotis, Some localizations of the spectral mapping theorem, Duke Math. J. 40 (1973), 651-660. Zbl0268.47004
7. [7] R. P. Boas, Entire Functions, Academic Press, 1954. Zbl0058.30201
8. [8] B. Bollobás, A property of hermitian elements, J. London Math. Soc. 4 (1971), 379-380. Zbl0239.46044
9. [9] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Ser. 2, Cambridge University Press, 1971. Zbl0207.44802
10. [10] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Ser. 10, Cambridge University Press, 1973. Zbl0262.47001
11. [11] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973. Zbl0271.46039
12. [12] H. N. Bojadjiev [K. N. Boyadzhiev], New applications of Bernstein inequality to the theory of operators: a local Sinclair lemma and a generalization of the Fuglede-Putnam theorem, in: Complex Analysis and Applications 85, Sofia, 1986, 97-104. 
13. [13] H. N. Bojadjiev [K. N. Boyadzhiev], Sinclair type inequalities for the local spectral radius and related topics, Israel J. Math. 57 (1987), 272-284. Zbl0648.47005
14. [14] A. Browder, On Bernstein's inequality and the norm of hermitian operators, Amer. Math. Monthly 78 (1971), 871-873. Zbl0224.47011
15. [15] I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators, Gordon and Breach, 1968. 
16. [16] M. J. Crabb and P. G. Spain, Commutators and normal operators, Glasgow Math. J. 18 (1977), 197-198. Zbl0351.47025
17. [17] H. R. Dowson, Some properties of prespectral operators, Proc. Roy. Irish Acad. 74 (1974), 207-221. Zbl0268.47034
18. [18] H. R. Dowson, T. A. Gillespie and P. G. Spain, A commutativity theorem for hermitian operators, Math. Ann. 220 (1976), 215-217. Zbl0305.47014
19. [19] D. Drissi, Quelques inégalités spectrales pour les opérateurs scalaires généralisés, Ph.D. thesis, Université Laval, 1993. 
20. [20] I. Erdelyi and R. Lange, Spectral Decompositions on Banach Spaces, Lecture Notes in Math. 623, Springer, 1977. Zbl0381.47001
21. [21] C. Foiaş, Une application des distributions vectorielles à la théorie spectrale, Bull. Sci. Math. 84 (1960), 147-158. Zbl0095.09905
22. [22] C. K. Fong, Normal operators on Banach spaces, Glasgow Math. J. 20 (1979), 163-168. 
23. [23] I. Gelfand, Zur theorie der Charaktere der abelschen topologischen Gruppen, Rec. Math. N.S. (Mat. Sb.) 9 (51) (1941), 49-50. Zbl67.0407.02
24. [24] E. Hille, On the theory of characters of groups and semi-groups in normed vector rings, Proc. Nat. Acad. Sci. 30 (1944), 58-60. Zbl0061.25305
25. [25] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, 1957. Zbl0078.10004
26. [26] I. Istrăţescu and V. Istrăţescu, A note on the Weyl's spectrum of an operator, Rev. Roumaine Math. Pures Appl. 15 (1970), 1445-1447. Zbl0209.15501
27. [27] V. È. Kacnel'son [V. È. Katsnel'son], A conservative operator has norm equal to its spectral radius, Mat. Issled. 5 (3) (17) (1970), 186-189 (in Russian). Zbl0226.47002
28. [28] S. Kantorovitz, Classification of operators by means of their operational calculus, Trans. Amer. Math. Soc. 115 (1965), 194-224. Zbl0127.07801
29. [29] G. K. Leaf, A spectral theory for a class of linear operators, Pacific J. Math. 13 (1963), 141-155. Zbl0121.33502
30. [30] B. Ja. Levin, Distribution of Zeros of Entire Functions, Amer. Math. Soc., 1964. 
31. [31] T. Pytlik, Analytic semigroups in Banach algebras and a theorem of Hille, Colloq. Math. 51 (1987), 287-294. Zbl0632.46043
32. [32] F. Riesz et B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Acad. Sci. Hongrie, Szeged, 1955. 
33. [33] W. Rudin, Functional Analysis, McGraw-Hill, 1973. 
34. [34] A. M. Sinclair, The norm of a hermitian element in a Banach algebra, Proc. Amer. Math. Soc. 28 (1971), 446-450. Zbl0242.46035
35. [35] D. R. Smart, Conditionally convergent expansions, J. Austral. Math. Soc. 1 (1960), 319-333. Zbl0104.08901
36. [36] B. G. Tillman, Vector-valued distributions and the spectral theorem for self-adjoint operators in Hilbert space, Bull. Amer. Math. Soc. 69 (1963), 67-71. 
37. [37] I. Vidav, Eine metrische Kennzeichnung der selbstadjungierten Operatoren, Math. Z. 66 (1956), 121-128. Zbl0071.11503
38. [38] P. Vrbová, On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23 (1973), 483-492. Zbl0268.47006
39. [39] K. K. Warner, A note on a theorem of Weyl, Proc. Amer. Math. Soc. 23 (1969), 469-471. Zbl0192.47501
40. [40] F. Wolf, Operators in Banach space which admit a generalized spectral decomposition, Nederl. Akad. Wetensch. Indag. Math. 19 (1957), 302-311. Zbl0077.31701

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