On a generalization of Lumer-Phillips' theorem for dissipative operators in a Banach space

• Autorzy: Driss Drissi
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

dissipative operators; local spectrum; semigroup of contraction operators

Kategorie tematyczne

• 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 130
• Numer: 1
• Strony: 1-7

Daty

wydano

1998

otrzymano

1996-02-20

poprawiono

1996-09-24

Twórcy

autor

Driss Drissi

• Department of Mathematics and Computer Sciences, Faculty of Sciences, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

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.