Domains of integral operators

Iwo Labuda; Paweł Szeptycki

Studia Mathematica (1994)

  • Volume: 111, Issue: 1, page 53-68
  • ISSN: 0039-3223

Abstract

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It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.

How to cite

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Labuda, Iwo, and Szeptycki, Paweł. "Domains of integral operators." Studia Mathematica 111.1 (1994): 53-68. <http://eudml.org/doc/216119>.

@article{Labuda1994,
abstract = {It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.},
author = {Labuda, Iwo, Szeptycki, Paweł},
journal = {Studia Mathematica},
keywords = {integral operator; proper domain; domains of integral operators; linear integral operators; Banach function spaces; proper domains},
language = {eng},
number = {1},
pages = {53-68},
title = {Domains of integral operators},
url = {http://eudml.org/doc/216119},
volume = {111},
year = {1994},
}

TY - JOUR
AU - Labuda, Iwo
AU - Szeptycki, Paweł
TI - Domains of integral operators
JO - Studia Mathematica
PY - 1994
VL - 111
IS - 1
SP - 53
EP - 68
AB - It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.
LA - eng
KW - integral operator; proper domain; domains of integral operators; linear integral operators; Banach function spaces; proper domains
UR - http://eudml.org/doc/216119
ER -

References

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  2. [B] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fund. Math. 3 (1922), 133-181. Zbl48.0201.01
  3. [D] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992. Zbl0776.42018
  4. [Dr] L. Drewnowski, On subseries convergence in some function spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 22 (1974), 797-802. Zbl0297.28014
  5. [F] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, 1966. Zbl0138.10207
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  7. [HS] P. R. Halmos and V. S. Sunder, Bounded Integral Operators in L 2 Spaces, Springer, 1978. Zbl0389.47001
  8. [K] V. B. Korotkov, Integral Operators, Nauka, Novosibirsk, 1983 (in Russian). Zbl0526.47015
  9. [MN] P. Meyer-Nieberg, Banach Lattices, Springer, 1991. Zbl0743.46015
  10. [N] E. M. Nikishin, Theorems of resonance and nonlinear operators, Uspekhi Mat. Nauk 25 (6) (1970), 129-191 (in Russian). Zbl0222.47024
  11. [R] S. Rolewicz, Metric Linear Spaces, PWN, Warszawa, 1972. 
  12. [P] B. de Pagter, A note on integral operators, Acta Sci. Math. (Szeged) 50 (1986), 225-230. Zbl0631.47018
  13. [Sc] A. R. Schep, Kernel operators, thesis, Leiden, 1977. 
  14. [Su] V. S. Sunder, Absolutely bounded matrices, Indiana Univ. Math. J. 27 (1978), 919-927. Zbl0419.47011
  15. [Z] A. C. Zaanen, Riesz Spaces, II, North-Holland, 1983. 

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