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

• Autorzy: Peter Vieten
• 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.

Kategorie tematyczne

• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 122
• Numer: 1
• Strony: 39-54

Daty

wydano

1997

otrzymano

1995-11-06

poprawiono

1996-03-04

Twórcy

autor

Peter Vieten

• Fachbereich Mathematik, Universität Kaiserslautern Erwin-Schrödinger-Str., 67663 Kaiserslautern, Germany,

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.