Compactness properties of an operator which imply that it is an integral operator
HTML articles powered by AMS MathViewer
- by A. R. Schep
- Trans. Amer. Math. Soc. 265 (1981), 111-119
- DOI: https://doi.org/10.1090/S0002-9947-1981-0607110-7
- PDF | Request permission
Abstract:
In this paper we study necessary and (or) sufficient conditions on a given operator to be an integral operator. In particular we give another proof of a characterization of integral operators due to W. Schachermayer.References
- J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964
- P. G. Dodds, $o$-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc. 214 (1975), 389–402. MR 385629, DOI 10.1090/S0002-9947-1975-0385629-1
- Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539
- Paul Richard Halmos and Viakalathur Shankar Sunder, Bounded integral operators on $L^{2}$ spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 96, Springer-Verlag, Berlin-New York, 1978. MR 517709
- Wilhelmus Anthonius Josephus Luxemburg, Banach function spaces, Technische Hogeschool te Delft, Delft, 1955. Thesis. MR 0072440
- W. A. J. Luxemburg and A. C. Zaanen, The linear modulus of an order bounded linear transformation. I, Nederl. Akad. Wetensch. Proc. Ser. A 74=Indag. Math. 33 (1971), 422–434. MR 0303337 W. Schachermayer, Integral operators on ${L^p}$-spaces. I, Indiana J. Math. (to appear).
- Helmut H. Schaefer, On the $\textrm {o}$-spectrum of order bounded operators, Math. Z. 154 (1977), no. 1, 79–84. MR 470748, DOI 10.1007/BF01215115
- Helmut H. Schaefer, Banach lattices and positive operators, Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York-Heidelberg, 1974. MR 0423039
- A. R. Schep, Kernel operators, Nederl. Akad. Wetensch. Indag. Math. 41 (1979), no. 1, 39–53. MR 528217
- A. R. Schep, Generalized Carleman operators, Nederl. Akad. Wetensch. Indag. Math. 42 (1980), no. 1, 49–59. MR 565943
- Adriaan Cornelis Zaanen, Integration, North-Holland Publishing Co., Amsterdam; Interscience Publishers John Wiley & Sons, Inc., New York, 1967. Completely revised edition of An introduction to the theory of integration. MR 0222234
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 265 (1981), 111-119
- MSC: Primary 47G05; Secondary 45P05, 47B05, 47B38
- DOI: https://doi.org/10.1090/S0002-9947-1981-0607110-7
- MathSciNet review: 607110