Warianty tytułu
Języki publikacji
Abstrakty
Using [1], which is a local generalization of Gelfand's result for powerbounded operators, we first give a quantitative local extension of Lumer-Philips' result that states conditions under which a quasi-nilpotent dissipative operator vanishes. Secondly, we also improve Lumer-Phillips' theorem on strongly continuous semigroups of contraction operators.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
1-7
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-02-20
poprawiono
1996-09-24
Twórcy
autor
- Department of Mathematics and Computer Sciences, Faculty of Sciences, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait, Drissi@math-1.sci.kuniv.edu.kw
Bibliografia
- [1] B. Aupetit and D. Drissi, Some spectral inequalities involving generalized scalar operators, Studia Math. 109 (1994), 51-66.
- [2] B. Aupetit and D. Drissi, Local spectrum theory and subharmonicity, Proc. Edinburgh Math. Soc. 39 (1996), 571-579)
- [3] F. F. Bonsall and J. Duncan, Numerical Ranges I and II, London Math. Soc. Lecture Note Ser. 2 and 10, Cambridge Univ. Press, 1971 and 1973.
- [4] I. Gelfand, Zur Theorie der Charaktere der Abelschen topologischen Gruppen, Mat. Sb. 9 (1941), 49-50.
- [5] E. Hille, On the theory of characters of groups and semigroups in normed vector rings, Proc. Nat. Acad. Sci. U.S.A. 30 (1944), 58-60.
- [6] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence, 1957.
- [7] G. Lumer and R. S. Phillips, Dissipative operators in Banach space, Pacific J. Math. 11 (1961), 679-698.
- [8] J. Zemánek, On the Gelfand-Hille theorems, in: Banach Center Publ. 30, Inst. of Math., Polish Acad. Sci., 1994, 369-385.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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