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

Peter Vieten

Studia Mathematica (1997)

  • Volume: 122, Issue: 1, page 39-54
  • ISSN: 0039-3223

Abstract

top
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.

How to cite

top

Vieten, Peter. "Four characterizations of scalar-type operators with spectrum in a half-line." Studia Mathematica 122.1 (1997): 39-54. <http://eudml.org/doc/216359>.

@article{Vieten1997,
abstract = {$C^0$-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.},
author = {Vieten, Peter},
journal = {Studia Mathematica},
keywords = {-scalar-type spectrality criteria; scalar-type operators},
language = {eng},
number = {1},
pages = {39-54},
title = {Four characterizations of scalar-type operators with spectrum in a half-line},
url = {http://eudml.org/doc/216359},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Vieten, Peter
TI - Four characterizations of scalar-type operators with spectrum in a half-line
JO - Studia Mathematica
PY - 1997
VL - 122
IS - 1
SP - 39
EP - 54
AB - $C^0$-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.
LA - eng
KW - -scalar-type spectrality criteria; scalar-type operators
UR - http://eudml.org/doc/216359
ER -

References

top
  1. [1] P. L. Butzer and H. Behrens, Semi-Groups of Operators and Approximation, Springer, Berlin, 1967. 
  2. [2] R. deLaubenfels, Unbounded scalar operators on Banach lattices, Honam Math. J. 8 (1986), 1-19. 
  3. [3] R. deLaubenfels, C 0 -scalar operators on cyclic spaces, Studia Math. 92 (1989), 49-58. Zbl0697.47034
  4. [4] R. deLaubenfels, Automatic extension of functional calculi, ibid. 114 (1995), 238-259. 
  5. [5] R. deLaubenfels and I. Doust, Functional calculus, integral representations, and Banach space geometry, Quaestiones Math. 17 (1994), 161-171. Zbl0815.47042
  6. [6] R. deLaubenfels and S. Kantorovitz, Laplace and Laplace-Stieltjes space, J. Funct. Anal. 116 (1993), 1-61. Zbl0795.47026
  7. [7] R. deLaubenfels and S. Kantorovitz The semi-simplicity manifold for arbitrary Banach spaces, ibid. 113 (1995), 138-167. Zbl0867.47028
  8. [8] J. Diestel and J. J. Uhl, Vector Measures, Amer. Math. Soc., Providence, 1977. 
  9. [9] I. Doust, Well-bounded and scalar type spectral operators on spaces not containing c 0 , Proc. Amer. Math. Soc. 105 (1989), 376-370. Zbl0674.47022
  10. [10] H. R. Dowson, Spectral Theory of Linear Operators, Academic Press, London, 1978. Zbl0384.47001
  11. [11] N. Dunford and J. T. Schwartz, Linear Operators, Part III, Wiley-Interscience, New York, 1971. 
  12. [12] J. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, Oxford, 1985. 
  13. [13] R. Hughes and S. Kantorovitz, Spectral analysis of certain operator functions, J. Operator Theory 22 (1989), 243-265. Zbl0761.47020
  14. [14] S. Kantorovitz, Characterization of unbounded spectral operators with spectrum in a half-line, Comment. Math. Helv. 56 (1981), 163-178. Zbl0472.47021
  15. [15] W. Ricker, Characterization of Stieltjes transforms of vector measures and an application to spectral theory, Hokkaido Math. J. 13 (1984), 299-309. Zbl0577.47037
  16. [16] H. H. Schäfer, A generalized moment problem, Math. Ann. 146 (1962), 326-330. Zbl0102.09905
  17. [17] P. Vieten, Holomorphie und Laplace Transformation banachraumwertiger Funktionen, Shaker, Aachen, 1995. 
  18. [18] D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1941. Zbl0063.08245

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.