Spectral properties of operator logarithms

Mathematische Zeitschrift

Volumn 245, Issue 4, 2003, Pages 761-779

  Haase, Markus ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346991602     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00209-003-0569-0     Document Type: Article

References (23)

1. Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F.: Vector-Valued Laplace Transforms and Cauchy Problems. Monographs in Mathematics. 96. Basel: Birkhäuser. xi, 523 p., 2001
2. Auscher, P., McIntosh, A., Nahmod, A.: Holomorphic functional calculi of operators, quadratic estimates and interpolation. Indiana Univ. Math. J. 46(2), 375-403 (1997)
3. Bade, W.G.: An operational calculus for operators with spectrum in a strip. Pacific J. Math. 3, 257-290 (1953)
4. Boyadzhiev, K.N.: Logarithms and imaginary powers of operators on Hubert spaces. Collect. Math. 45, 287-300 (1994)
5. ∞ functional calculus. J. Austral. Math. Soc. Ser. A 60, 51-89 (1996)
6. Dore, G., Venni, A.: On the closedness of the sum of two closed operators. Math. Z. 196, 189-201 (1987)
7. Dunford, N., Schwartz, J.T.: Linear Operators. I. General Theory. (Pure and Applied Mathematics. Vol. 6) New York and London: Interscience Publishers. XIV, 858 p., 1958
8. Engel, K.-J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics. 194. Berlin: Springer, xxi, 586 p., 2000
9. ∞-calculus. Semigroup Forum 66, 288-304 (2003)
10. Haase, M.: The Functional Calculus for Sectorial Operators and Similarity Methods. PhD thesis, Universität Ulm, 2003
11. Hille, E., Phillips, R.S.: Functional Analysis and Semi-Groups. 3rd printing of rev. ed. of 1957. American Mathematical Society, Colloquium Publications, Vol. XXXI. Providence, Rhode Island: The American Mathematical Society. XII, 808 p., 1974
12. Kato, T.: Perturbation Theory for Linear Operators. Reprint of the corr. print, of the 2nd ed. 1980. Classics in Mathematics. Berlin: Springer-Verlag, xxi, 619 p., 1995
13. Merdy, C.L.: The similarity problem for bounded analytic semigroups on Hilbert space. Semigroup Forum 56, 205-224 (1998)
14. Martinez Carracedo, C., Sanz Alix, M.: The theory of fractional powers of operators. North-Holland Publishing Co., Amsterdam, 2001
15. ∞ functional calculus. In: Miniconference on operator theory and partial differential equations (North Ryde, 1986), Austral. Nat. Univ., Canberra, 1986, pp. 210-231
16. Monniaux, S.: A new approach to the Dore-Venni theorem. Math. Nachr. 204, 163-183 (1999)
17. Nollau, V.: Über den Logarithmus abgeschlossener Operatoren in Banachschen Räumen. Acta Sci. Math. (Szeged) 30, 161-174 (1969)
18. Okazawa, N.: Logarithms and imaginary powers of closed linear operators. Int. Eqs. Oper. Theor. 38, 458-500 (2000)
19. Prüss, J.: Evolutionary Integral Equations and Applications.Monographs in Mathematics. 87. Basel: Birkhäuser Verlag. xxvi, 366 p., 1993
20. Prüss, J., Sohr, H.: On operators with bounded imaginary powers in Banach spaces. Math. Z. 203, 429-452 (1990)
21. Uiterdijk, M.: Functional Calculi for Closed Linear Operators. PhD thesis, Technische Universiteit Delft, 1998
22. 0-groups. Int. Eqs. Oper. Theor. 36, 349-369 (2000)
23. Wolff, M.: A remark on the spectral bound of the generator of semigroups of positive operators with applications to stability theory. In: Functional analysis and approximation (Oberwolfach, 1980), volume 60 of Internat. Ser. Numer. Math., Birkhäuser, Basel, 1981, pp. 39-50