Compactness properties of an operator which imply that it is an integral operator

Schep, A. R.

doi:10.1090/S0002-9947-1981-0607110-7

Compactness properties of an operator which imply that it is an integral operator
HTML articles powered by AMS MathViewer

by A. R. Schep PDF

Trans. Amer. Math. Soc. 265 (1981), 111-119 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

Integral operators on

-spaces

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