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1997 | 122 | 1 | 39-54
Tytuł artykułu

Four characterizations of scalar-type operators with spectrum in a half-line

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
$C^0$-scalar-type spectrality criterions for operators A whose resolvent set contains the negative reals are provided. The criterions are given in terms of growth conditions on the resolvent of A and the semigroup generated by A. These criterions characterize scalar-type operators on the Banach space X if and only if X has no subspace isomorphic to the space of complex null-sequences.
Słowa kluczowe
Czasopismo
Rocznik
Tom
122
Numer
1
Strony
39-54
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-11-06
poprawiono
1996-03-04
Twórcy
autor
  • Fachbereich Mathematik, Universität Kaiserslautern Erwin-Schrödinger-Str., 67663 Kaiserslautern, Germany, vieten@mathematik.uni-kl.de
Bibliografia
  • [1] P. L. Butzer and H. Behrens, Semi-Groups of Operators and Approximation, Springer, Berlin, 1967.
  • [2] R. deLaubenfels, Unbounded scalar operators on Banach lattices, Honam Math. J. 8 (1986), 1-19.
  • [3] R. deLaubenfels, $C^0$-scalar operators on cyclic spaces, Studia Math. 92 (1989), 49-58.
  • [4] R. deLaubenfels, Automatic extension of functional calculi, ibid. 114 (1995), 238-259.
  • [5] R. deLaubenfels and I. Doust, Functional calculus, integral representations, and Banach space geometry, Quaestiones Math. 17 (1994), 161-171.
  • [6] R. deLaubenfels and S. Kantorovitz, Laplace and Laplace-Stieltjes space, J. Funct. Anal. 116 (1993), 1-61.
  • [7] R. deLaubenfels and S. Kantorovitz The semi-simplicity manifold for arbitrary Banach spaces, ibid. 113 (1995), 138-167.
  • [8] J. Diestel and J. J. Uhl, Vector Measures, Amer. Math. Soc., Providence, 1977.
  • [9] I. Doust, Well-bounded and scalar type spectral operators on spaces not containing $c_0$, Proc. Amer. Math. Soc. 105 (1989), 376-370.
  • [10] H. R. Dowson, Spectral Theory of Linear Operators, Academic Press, London, 1978.
  • [11] N. Dunford and J. T. Schwartz, Linear Operators, Part III, Wiley-Interscience, New York, 1971.
  • [12] J. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, Oxford, 1985.
  • [13] R. Hughes and S. Kantorovitz, Spectral analysis of certain operator functions, J. Operator Theory 22 (1989), 243-265.
  • [14] S. Kantorovitz, Characterization of unbounded spectral operators with spectrum in a half-line, Comment. Math. Helv. 56 (1981), 163-178.
  • [15] W. Ricker, Characterization of Stieltjes transforms of vector measures and an application to spectral theory, Hokkaido Math. J. 13 (1984), 299-309.
  • [16] H. H. Schäfer, A generalized moment problem, Math. Ann. 146 (1962), 326-330.
  • [17] P. Vieten, Holomorphie und Laplace Transformation banachraumwertiger Funktionen, Shaker, Aachen, 1995.
  • [18] D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1941.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv122i1p39bwm
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