The adjoint of a positive semigroup

J. M. A. M. Van Neerven; B. de Pagter

Compositio Mathematica (1994)

  • Volume: 90, Issue: 1, page 99-118
  • ISSN: 0010-437X

How to cite

top

Van Neerven, J. M. A. M., and de Pagter, B.. "The adjoint of a positive semigroup." Compositio Mathematica 90.1 (1994): 99-118. <http://eudml.org/doc/90270>.

@article{VanNeerven1994,
author = {Van Neerven, J. M. A. M., de Pagter, B.},
journal = {Compositio Mathematica},
keywords = {positive -semigroup on a Banach lattice; projection band; lattice semigroup},
language = {eng},
number = {1},
pages = {99-118},
publisher = {Kluwer Academic Publishers},
title = {The adjoint of a positive semigroup},
url = {http://eudml.org/doc/90270},
volume = {90},
year = {1994},
}

TY - JOUR
AU - Van Neerven, J. M. A. M.
AU - de Pagter, B.
TI - The adjoint of a positive semigroup
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 90
IS - 1
SP - 99
EP - 118
LA - eng
KW - positive -semigroup on a Banach lattice; projection band; lattice semigroup
UR - http://eudml.org/doc/90270
ER -

References

top
  1. [AB] C.D. Aliprantis and O. Burkinshaw, Positive Operators, Pure and Applied Math. 119, Academic Press, 1985. Zbl0608.47039MR809372
  2. [BB] P.L. Butzer, and H. Berens, Semigroups of Operators and Approximation, Springer-Verlag, New York (1967). Zbl0164.43702MR230022
  3. [C1] Ph. Clément, O. Diekmann, M. Gyllenberg, H.J.A.M. Heijmans and H.R. Thieme, Perturbation theory for dual semigroups, Part I: The sun-reflexive case, Math. Ann.277 (1987) 709-725; Part II: Time-dependent perturbations in the sun-reflexive case, Proc. Roy. Soc. Edinb.109A (1988) 145-172; Part III: Nonlinear Lipschitz perturbations in the sun-reflexive case, In: G. Da Prato, M. Iannelli (eds.), Volterra Integro Differential Equations in Banach Spaces and Applications, Longman, (1989) 67-89; Part IV: The intertwining formula and the canonical pairing, In: Semigroup Theory and Applications, Lecture Notes in Pure and Applied Mathematics, Vol. 116, Marcel Dekker Inc., New York- Basel (1989); Part V: Variation of constants formulas, In: Semigroup Theory and Evolution Equations, Lecture Notes in Pure and Applied Mathematics, Vol. 135, Marcel Dekker Inc., New York -Basel (1991). Zbl0675.47036MR901713
  4. [GN] A. Grabosch and R. Nagel, Order structure of the semigroup dual: a counterexample, Indag. Math.92 (1989) 199-201. Zbl0697.47037MR1005051
  5. [GM] C.C. Graham and O.C. McGehee, Essays in Commutative Harmonic Analysis, Springer-Verlag, New York, Heidelberg, Berlin (1979). Zbl0439.43001MR550606
  6. [M] P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, Berlin, Heidelberg, New York (1991). Zbl0743.46015MR1128093
  7. [MG] H. Milicer-Gruzewska, Sur la continuité de la variation, C. R. Soc. Sci. de Varsovie, 21 (1928) 164-177. JFM57.1390.02
  8. [Na] R. Nagel (ed.), One-parameter Semigroups of Positive Operators, Springer Lect. Notes in Math. 1184 (1986). Zbl0585.47030MR839450
  9. [Ne] J.M.A.M. van Neerven, The Adjoint of a Semigroup of Linear Operators, Lect. Notes in Math. 1529, Springer-Verlag, Berlin, Heidelberg, New York (1992). Zbl0780.47026MR1222650
  10. [NP] J.M.A.M. van Neerven and B. de Pagter, Certain semigroups on Banach function spaces and their adjoints, In: Semigroup Theory and Evolution Equations. Lecture Notes in Pure and Applied Mathematics, Vol. 135, Marcel Dekker Inc., New York- Basel (1991). Zbl0745.47027MR1164664
  11. [Pa1] B. de Pagter, A characterization of sun-reflexivity, Math. Ann.283 (1989) 511-518. Zbl0696.47039MR985246
  12. [Pa2] B. de Pagter, A Wiener-Young-type theorem for dual semigroups, Appl. Math.27 (1992) 101-109. Zbl0895.47030MR1184882
  13. [Ph] R.S. Phillips, The adjoint semi-group, Pac. J. Math.5 (1955) 269-283. Zbl0064.11202MR70976
  14. [P1] A. Plessner, Eine Kennzeichnung der totalstetigen Funktionen, J. f. Reine u. Angew. Math.60 (1929) 26-32. Zbl55.0143.03JFM55.0143.03
  15. [S] H.H. Schaefer, Banach Lattices and Positive Operators, Springer Verlag, Berlin, Heidelberg, New York (1974). Zbl0296.47023MR423039
  16. [WY] N. Wiener and R.C. Young, The total variation of g(x + h) - g(x), Trans. Am. Math. Soc.35 (1933) 327-340. Zbl0006.19401MR1501686JFM59.0284.03
  17. [Z] A.C. Zaanen, Riesz Spaces II, North Holland, Amsterdam (1983). Zbl0519.46001MR704021

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.